The Architecture and Sacred Temple Geometry of Japanese Buddhist Temples
Key Terms
Japanese Architecture
Japanese Temple Architecture
Japanese Traditional Mathematics
Wasan
Japanese Buddhist Temples
Pagodas
Stupa
Chorten
Wayō, Daibutsuyō, Zenshūyō, Setchūyō
Sangaku
Fukagawa Hidetoshi
Tony Rothman
Don Pedoe
J. Rigby
Pagoda, ta, mandala, Sumeru, Yicihui pillar, Yongningsi, Songyuesi
Diagram of a Gorinto
Hokyointo Pagoda
Tahoto Pagoda
Sotobo
Square
Circle
Regular Polyhedra
Cube, Sphere, Pyramid, SemiSphere, Chintamani
Earth, Water, Fire, Air, Universe
Plato and Aristotle
Shingon, Kukai, 5 Stories, Circle
Tendai, Saicho, 3 stories, Square
Diamond World, Matrix World
Adrian Snodgrass
Tracy Miller
Gojunoto
The Architecture of Japanese Buddhist Temples
December 19, 2021
Natalie Solari
Overview:
This exhibition takes a closer look at the main buildings of five Japanese Temple Complexes. Temples are the places of worship in Japanese Buddhism, and are also used to display sacred Buddhist objects. It is believed that Buddhist images could have been brought to Japan as early as 522 (Beguin). Japanese Buddhism has made an abundant impact on Japanese culture and continues to influence society today. The architectural elements of Buddhist temples are meant to embody themes and teachings of Buddhism.
Most Buddhist temples in Japan are designed around four main architectural styles: Wayō, Daibutsuyō, Zenshūyō, and Setchūyō. Temples designed in the wayō style take a minimalistic approach to architecture. Natural timber and generally plain materials are used. Wayō architecture was made during the Heian period, between 794 CE and 1185 CE. Typically these structures feature thin columns and a low ceiling. A beam is run through the columns to reinforce the top parts of columns. The wayō style emphasizes more Japanese-style architecture than the features of Chinese-style architecture. Inside the structures inner space divisions are fluid, many feature screens and thin. A true connection is meant to be felt between the interior and exterior of the building.
In the late 12th and early 13th century CE, a more monumental style emerged. The daibutsuyō style was based on Song Dynasty architecture. Daibutsuyō style architecture is characterized by thick woodwork and penetrating tie beams. The ends of the penetrating tie beams are decorated with moldings also known as ‘kurigata’. The thick woodwork of the structure is typically left exposed to show its elements. This style takes a grander approach than the wayō style. Daibutsuyō style architecture utilizes horizontal elements.
Zenshūyō is another style that emerged in the late 12th or early 13th century CE. Zenshūyō style temples are based on contemporary Chinese architecture derived from the Song Dynasty. The style is named after the Zen sect of Buddhism that was introduced to Japan. These temples typically incorporate earthen floors, decorative curved pent roofs, pointed windows, and paneled doors. Slim columns and low ceilings are used to create calming spaces for meditating.The complexes have a generally linear layout. Kōzan-ji’s butsuden is the oldest extant building in the Zenshūyō style in Japan.
The last style of temple architecture incorporates a fusion of elements from the three other styles. This style was called setchūyō, and was used during the Muromachi period. By the end of the Muromachi period, Japanese Buddhist architecture and construction methods had been perfected and building types were conventionalized.
Although the temples are designed around a few different styles, there are some key features that distinguish these Japanese Buddhist temples. Characteristics of most Japanese Temples include post and lintel support, a gentle curved roof, and thin walls. The use of a single central pillar or column. embodies the Axis Mundi of Buddhism. Having the cardinal directions reflected through the structure is important. The most prominent examples of the iconic form are represented in Pagodas and Indian Stupas. Many of these temples are incorporated into complexes with several other structures that include a main hall, a pagoda, and other facilities for prayer and meditation. Many of these temple complexes are surrounded by a large wall and gates. Entering the complex is supposed to feel like a journey through meditation. These spaces are intended to evoke feelings of peace.
Description: The Phoenix Hall is the main hall at Byodo-in temple. Phoenix Hall was established in 1053 CE, in the late Heian period. The hall houses the Shrine of the Buddha Amida. Phoenix Hall is an example of Wayo architecture as well as shinden-zukuri, the style of Japanese nobility’s residences. Phoenix Hall incorporates unique architecture which consists of the main corridor, left and right wing corridors, and a tall corridor. The shape of the building resembles the body and spreading wings of the Phoenix. Its main corridor faces south to bring in sunlight and opens on to the pond of a beautiful garden. A Pure Land style garden is centered around the Ajino-ike Pond, that reflects the architecture of the structure. A true connection is felt between the interior and exterior of the hall.
The central corridor is topped by a hip-and-gable roof and also features a pent roof enclosure. Hip-and-gable roofs are characterized by a rounded hip roof that cascades down on all sides, and a triangular gable at each end. Two phoenix statues are positioned on top of the roof. The stairs leading to the main entrance are made of marble, but the structure of the hall is made of wood. The doors and walls are decorated by richly colored paintings, and the ceiling and pillars are also covered with colorful patterns. The brightly colored exterior clashes with the minimalistic Wayō style, but the gentle lines of the exterior and openness of the interior hold on to its values.
The Great Buddha Hall atTodai-ji temple complex displays the grand features of the daibutsuyō architectural style. The Great Buddha hall houses the world’s largest bronze Buddha Vairocana statue. This Buddhist temple complex was once one of the powerful Seven Great Temples. Two towering guardians sit on top of the massive entryway of the temple, protecting the great Buddha. The great architects of Todaiji temple complex developed the Yakushiji axial plan with paired pagodas into one of greater complexity (Ikeuchi 2007). The hall was erected in the early 8th century CE, and later reconstructed in 1709. The Great Buddha hall was built at a very large scale, displaying the power and prestige of the imperial house of Japan. Columns are arrayed throughout the rectangular base to represent universal order. Many horizontal braces are run through vertical posts called Nuki to make the structure solid.
As a daibutsuyō style hall, structural elements are left exposed without the covering of a ceiling as decoration. The vast structure is made entirely of wood, commonly seen in Japanese architecture. Building structures out of wood was seen as a way to celebrate life. A gently sloping roof was used to help blend in the large structure to its natural surroundings. The roof tiles were carefully crafted to channel water to prevent erosion.
Kondô Hall is the main hall of Fudôin Temple. This hall was built in the Zenshūyō architectural style. Kondô at Fudôin is an Important Cultural Property, as one of the few remaining historic structures in Hiroshima. After careful studies of historic documents and writing found on the ceilings, it is believed that Kondô Hall was originally built in Yamaguchi in 1540 at the site of Koshakuji Temple. The Kondô Hall was later relocated to its current location in Hiroshima when Ekei expanded the temple. The structure miraculously survived the atomic bomb drop in 1945 on the city. Kondô Hall is the only National Treasure in Hiroshima City. The structure features massive beams, the longest being over 7 meters (Davies). Kondô Hall has a irimoya, a unique combination of gable and hip roof with a mokoshi (an extra roof). The grand roof casts shadows on the ground below, adding to the sacred atmosphere. Oversized eaves give the interior a characteristic dimness, which contributes to the temple’s sacred atmosphere. Paintings of angels and dragons fill the ceilings. This structure appears less conspicuous and more meditative than the other styles of architecture. This structure houses the statue of Yakushi Nyorai, also known as the Medicine Buddha. The statue was carved by the pioneer sculptor Jocho, who was a famous Japanese sculptor in the early 11th century.
Title: Temple of Golden Pavilion Kinkaku-ji Category: Japanese Buddhist Architecture Architectural style: Setchūyō Location: Kyoto, Japan Author Name: Ondraness Medium: image/jpeg Date of Creation: 9 September 2019 Dimensions: 5,312 × 2,988 pixels Image Link:https://commons.wikimedia.org/wiki/File:Golden_pavilion,_Kinkakuji.jpg
Description: Kinkaku-ji is located on the Rokuon-ji temple complex. This Japanese Buddhist temple exhibits the Setchūyō architectural style used to design Japanese Buddhist temples. Setchūyō emerged in Japan during the Muromachi period, characterized by the fusion of elements from preceding styles. Buddhist temples in Japan follow a general structure of columns and lintels that support a large and gently curved roof. Kinkaku-ji is known for its gold leaf exteriors of the upper two floors. In Pure Land Buddhism gold represents spiritual purity which is reflected through the structure.
Each level of the temple incorporates a different style of architecture. Shiden style is displayed on the first floor, an open space decorated with natural wood pillars and white plaster. This floor emphasises the surrounding landscape and garden design. The second floor of the temple embodies the style used in samurai residences. Paintings of birds, clouds, and instruments cover the ceilings and walls. The third and final floor is built in the style of a Chinese Zen Hall, with lavish decoration. The sacred relics of the Buddha are kept in this sacred space. A large thatched pyramid roof covers the structure. The temple is topped with a bronze phoenix ornament.
Kakurin-ji Temple is the 20th temple of the Shikoku Ohenro Pilgrimage. Kakurin-ji is incredibly difficult to reach due to its location at the top of a steep mountain. Sitting at 550 meters elevation, the temple is the 5th highest structure on the pilgrimage route. The Main Hall at Kakurin-ji Temple embodies the Setchūyō architectural style used to design Japanese Buddhist temples. The Main Hall, which was named a National Treasure of Japan, was built in 1397. The Main Hall was designed with the East Asian hip-and-gable roof, the structure stands tall off the ground and appears to float. The roof is a bold feature of the structure. With the location high on a mountain and the unique architecture a sacred Buddhist space is created. A beautiful three-storey pagoda sits to the right of the Main Hall.
Bibliography:
Images:
Daibutsuden (Great Buddha Hall), Todai-ji temple complex
Young, David; Young, Michiko (2007) [2004]. “The Art of Japanese Architecture.” Architecture and Interior Design (illustrated, revised ed.). Tuttle Publishing. ISBN 978-0-8048-3838-2.
Jaffe, Richard M. 2006. “Buddhist Material Culture, ‘Indianism,’ and the Construction of Pan-Asian Buddhism in Prewar Japan.” Material Religion: The Journal of Objects, Art and Belief 2 (3): 266–92. doi:10.2752/174322006778815126.
Mizuta, MiyaElise. “Luminous Environment: Light, Architecture and Decoration in Modern Japan.” Japan Forum 18, no. 3 (November 2006): 339–60. doi:10.1080/09555800600947223.
Cabeza-Lainez, Joseph M, and Jose M Almodovar-Melendo. “Daylight, Shape, and Cross-Cultural Influences Through the Routes of Discoveries: The Case of Baroque Temples.” Space and Culture 21, no. 4 (November 2018): 375–94. https://doi.org/10.1177/1206331217749764.
Kaneta, Kiyoshi. “Structural Reinforcement of Historic Wooden Temples in Japan.” Bulletin of the Association for Preservation Technology 12, no. 1 (1980): 75–91. https://doi.org/10.2307/1493875.
Yiengpruksawan, Mimi Hall. “The Phoenix Hall at Uji and the Symmetries of Replication.” The Art Bulletin 77, no. 4 (1995): 647–72. https://doi.org/10.2307/3046141.
Ikeuchi, K., Oishi, T., Takamatsu, J. et al. The Great Buddha Project: Digitally Archiving, Restoring, and Analyzing Cultural Heritage Objects. Int J Comput Vis 75, 189–208 (2007). https://doi.org/10.1007/s11263-007-0039-
“Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chongnimsa and Kamunsa Buddhist Temples.”
TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD
Koji Miyazaki Professor Emeritus, Kyoto University, Japan
Archi-Cultural Translations through the Silk Road 2nd International Conference, Mukogawa Women’s Univ., Nishinomiya, Japan, July 14-16, 2012 Proceedings
Japanese Buddhist Architecture mainly includes the architecture of Buddhist temples which was influenced by the architectural styles from China. Earlier, the attempts were to make the Buddhist architecture as original as it was looked in China but gradually the buildings were localized due to the problems posed by local weather and Japanese tastes.
Historical development of Japanese Buddhist Architectures
The development of Japanese Buddhist Architectures can be broadly divided into the following periods
Asuka and Nara Periods
The Buddhism and the Buddhist architecture were literally imported from China via Korea in the 6th century. As the Buddhism was introduced in Japan, the Buddhist temples were started to build in the country but due to the hostile behavior of supporter of the local kami, the buildings were no longer stand by itself and there are no written records of the architectural styles of that period.
But later the Buddhism got its support from the Prince Shotoku. He ordered the construction of Buddhist temple, Shitennoji in Osaka (593) and Horyu-ji near his palace in Ikaruga (603). During this period, the temple layout was strictly prescribed and followed. This act helped to maintain the architectural style uniform. In this period the main gate was constructed facing south and the most sacred area surrounded by a semi-enclosed roofed corridor accessible through a middle gate. The temple complex also contains the main hall with Buddha statue, and pagoda which houses sacred objects. The other structures include a lecture hall, a belfry, a sutra repository, priests and monks quarters and bathhouse.
Nara Period observed quite different architectural development. The temple structures, such as pagodas and main halls, had increased significantly in size. The placement of the pagoda moved to a more peripheral location and the roof bracketing system increased in complexity as roofs grew larger and heavier.
In the 8th century, Kami worship and Buddhism was reconciled and thus shrine-temples were founded to support both groups. This coexistence of Buddhism and Kami worship continued until the Kami and Buddhas Separation Order of 1868.
Heian period
In this period, Buddhism was more localized with addition Japanese elements, local beliefs. With this localization Fujiwara no Michinaga and retired Emperor Shirakawa erected new temples and hence developed Jodo-Kyo architectureand the new Wayo architectural style.
In the early period, Rokushu architectonic traditions were also observed. This style of architecture was developed only in the plains but in mountainous areas, it was an original style. The architectural style was characterized by the simplicity which uses local resources like natural timber.
The architecture includes a main hall which is generally divided into two parts; an outer area for novices and an inner area for initiates. The roof is a hip and gable which covers both the areas. The floor is little raised which is made up of wood.
Kamakura and Muromachi periods
In Kamakura period, Daibutsu style and the Zen style of architectural designemerged. The first style represents the antithesis of the simple and traditional Wayo style while the Zen style characterized as earthen floors, subtly curved pent roofs, cusped windows, and paneled doors.
In Muromachi periods, the above-mentioned style of architecture was often combined to form the new style of architecture, Eclectic style of architecture.
Other notable periods in the history of the development of Japanese Buddhist architecture were Azuchi-Momoyama and Eddo periods, and Meiji period. In these periods the Buddhist architectures were also developed accordingly focusing on the local beliefs and use of local resources.
General features of Japanese Buddhist Architectures
Actually, the architectural styles of Japanese Buddhist buildings were imported from China and various other Asian countries. With time, these architectural styles were localized in order to suit the Japanese tastes, and the local resources and weather.
Japanese architects have used a locally available material, mainly wood in various forms. It is hard to see the buildings that use stones except for certain specific uses as in temple podia and pagoda foundations.
Almost all the buildings share the common general structure: columns and lintels to support a large and gently curved roof. The walls are also paper thin, which is often movable. We can notice that the arches and barrel roofs are completely absent. It is recorded that gable and eave curves are gentler that in China and columnar entasis limited.
The most impressive component of the Japanese Buddhist architecture is the roof. The roof has the slightly curved eaves that extend far beyond the walls, covering verandas. These oversize eaves give the interior a characteristic dimness, which contributes to the temple’s atmosphere. The building normally consists of a single room at the center called Moya.
As it is already mentioned that the inner walls are paper thin and often movable, the room size can be modified as per required. Hence, the large, single space offered by the main hall can, therefore, be altered according to the need.
Sometimes the architecture is shared by both sacred and profane building structures. Therefore, these architectural features made it easy to convert a lay building into the Buddhist temple. The popular Horyu-Ji Buddhist temple in Nara Prefecture is the excellent example. This building was once used to be the mansion for the noblewoman.
At the beginning of the seventeenth century, Tokugawa Ieyasu completed the unification of Japan. His shogunate ruled for more than 250 years and oversaw a period of peace, but with restricted foreign contact. Poetry, music and literature flourished during this time of relative isolation. A unique form of Japanese culture of the period was sangaku — a combination of mathematics and art on votive tablets. Illustrated wooden shingles up to several metres across bearing geometry problems were hung from Shinto shrines and Buddhist temples for public display. Many historical sangaku answers appeared on tablets without proof, perhaps to demonstrate the mathematical prowess of the presenter. And their sacred context remains unclear: the tablets might have been educational or may have signalled gratitude for divine assistance in solving a mathematical problem. Of the thousands of tablets created, only a fraction survive, and they have received scant coverage in histories of Japanese mathematics.
Now Fukagawa Hidetoshi, a mathematics teacher, and writer Tony Rothman present a collection of sangaku problems in their book, Sacred Mathematics. The puzzles range from simple algebra within the grasp of any intermediate-school student, to challenging problems that require graduate-school mathematics to solve. Copious illustrations and many detailed solutions show the scope, complexity and beauty of what was tackled in Japan during the Tokugawa shogunate.
Credit: A. SHINBUN
The book offers a feast for recreational geometers looking for fun new problems, presented and solved in clever ways. Yet the authors give little insight into how these problems were solved at the time, or whether unique Japanese methods were involved. The sangaku figures are mostly redrawn with modern notation, and solutions offered in the compact form of present-day Western mathematics. Illustrating traditional Japanese and modern Western methods side by side would have been instructive. The book thus achieves only limited success in showcasing sangaku as exemplars of a uniquely Japanese style of mathematics, because that style is never elucidated.
Fukagawa and Rothman illuminate the mathematics more than the history and context of the tablets. Citations to mathematical theorems abound, yet references supporting their historical claims are absent. More seriously, the historical commentary reflects a romantic bias that a unique Japanese culture flowered because of its complete isolation. The book states, for instance, that “a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in the western mathematics”. This generalization is historically unsupported, and obstructs an accurate consideration of the interplay of factors that drove the development of Japanese mathematics.
Along similar lines, the authors also dismiss the millennium that preceded the seventeenth century as “a dark age” paralleling that in Europe, during which relatively little was accomplished in mathematics. By ignoring the medieval Islamic world, they fall into the same trap as Eurocentric mathematical historians who focus exclusively on ancient Greece and modern Europe. This omission undermines their discussion of the Chinese foundation of Japanese mathematics. World-leading achievements in mathematics, science and technology — even astronomers from Persia — reached China during the medieval period by the Silk Road and other routes. The book describes in great detail how Seki Takakazu, “Japan’s most celebrated mathematician”, calculated π to 11 digits in the eighteenth century. But it does not mention Jamshid Mas’ud al-Kashi, who determined π correctly to 16 digits some three centuries earlier while residing in Samarkand (in what is now Uzbekistan), one of the most important cities along the Silk Road.
The complex events that followed Japan’s opening to the West after the shogunate’s end in the 1860s are given similarly short shrift. The response of Japanese mathematics to this influx of ideas is dispatched with the glib statement that “resistance was futile”. By quoting a science-fiction character from Star Trek that annihilates everything in its path by assimilation, Fukagawa and Rothman trivialize Japan’s complicated process of reintegration with the international community, and miss the opportunity to shed light on how its early mathematics contributed to Japan’s present-day leadership in science and technology.
Review Sacred Mathematics Japanese Temple Geometry
Although timber is rarely used as a construction material in modern-day China, history tells us that it was used extensively in the past. The Chinese used timber as roofing and flooring material and incorporated timber beams and columns in their structures. The structural system mainly relied on the timber framework as the walls were non-load bearing. This form of construction did not restrict the location of openings in the structure and hence there was more freedom to decide where the windows could be placed, without worrying too much about the safety and stability of the structure. It was deemed essential to paint the framework to prevent the onset of rot in the timber. With time, the painting of the pagodas became an integral part of the Chinese architectural style. Colours are very symbolic in Chinese architecture and are used to mark the importance and function of the structure. The colour yellow is associated with nobility and was used in royal structures. Red and green are considered colours of life.
The origin of the pagodas in China dates back to the period of the advent of Buddhism from India. The pagodas were meant to be religious monuments which preserved holy objects ranging from relics and keepsakes to sacred documents. The Chinese architects integrated the Indian style of constructing stone stupas into the traditional architectural style and came up with a suitable design. The pagodas were tall and symmetric. They were built using different materials- stone, bricks, wood, iron, glazed tiles and occasionally, even gold! They were multi-storeyed with the number of floors always being an odd number. The minimum number of floors was 3 and most of them went up to 9, or even more. At the apex, pagodas were topped with a steeple – a symbol of the power of heaven. There are some speculations as to why the pagodas always had many storeys, which I have mentioned below.
Among the religious buildings in China, I am most enchanted by their pagodas, particularly the Yingxian Pagoda which also goes by the name of Sakyamuni. This used to be the tallest wooden pagoda in the world until 2007, when the construction of the Tianning pagoda (Changzou temple) was completed. The Sakyamuni Pagoda is about 67.31m in height, while the one at Changzou is more than two times taller (153.79m).
Housed in the Fogong Temple, the Sakyamuni pagoda was constructed in 1056 A.D. during the reign of the Liao Dynasty. The pagoda is erected on a stone platform measuring 4 metres in height. The pagoda itself is built entirely out of wood obtained from the Xingan larch trees that were found in abundance in Northern China. When you look at the Sakyamuni pagoda from outside, it appears to be a 5 storeyed structure; although in reality it is 9 storeys high. This is because the four mezzanine layers are concealed within the five outer storeys. The ground floor is topped by two tiers of eaves.
A model of the Sakyamuni pagoda at the Hong Kong Heritage Museum
The plan of the building is octagonal in shape and consists of two concentric rings of columns. The columns are not vertical, but inclined to the apex of the pagoda. The angle of inclination depends on the position of the columns in the pagoda, and hence on the load carried.
Concentric rings of columns (source: Lam et al.)Vertical section of the pagoda (source: Lam et al.)
A series of tie beams connects the columns in each ring. An individual beam is connected to a column by means of a slot which forms the connection (tenon and mortise joint). The connections are comprised of only tenon and mortise joints and dou gong brackets. A dou gong bracket is composed of three components – a wooden block called ‘dou’, a lever arm called ‘ang’ and a short arm called ‘gong’.
In the Yingxian pagoda, the dugong brackets are arranged in layers so that they can transfer the loads from the roof to the subsequent storeys. There are 54 different types of dou gong brackets used in the pagoda. The dou gong system is arranged akin to a basket of flowers. The layered dou gong bracket system symbolizes a hierarchical system and is therefore used only in buildings of importance. The number of layers of these brackets is proportional to the degree of importance of the building. In the Yingxian pagoda, they are set under the overhanging eaves of the building and between the top of each column and cross beam.
The connections between the wooden members were originally supposed to be tight fitted joints. But as it is widely known, timber undergoes shrinkage with time and dries out. Due to this the connections became loose but are still kept together by gravity loads. In the event of an earthquake, the connections are able to move and dissipate energy and hence contribute to the high seismic resistance of the Yingxian pagoda. Additional stability is derived from the relatively short columns. Records reveal that during a high intensity earthquake lasting seven days during the reign of the Yuan Dynasty, the pagoda stood firm. Even when the Yingxian County area was affected by the severe earthquakes in Xingtai and Tangshan of Hebei Province and in Helinger of Inner Mongolia, the wooden pagoda did not suffer any major damage. In 1996, this structure was listed as a UNESCO World Heritage Site.
Although this wooden pagoda has been able to withstand several earthquakes, severe winds, lightning strikes, high amounts of precipitation and wars in the past 958 years, it is highly unlikely that it is going to last for another millennium. Column heads and ridge beams are twisted and broken. Some of the interior columns have developed cracks. The tower of the pagoda leans slightly to the north-east. There is an obvious tilt in the first and second floors and the scientific community has issued warnings about the inability of the structure to withstand a violent storm or an earthquake. In 2001, the State Administration of Cultural Heritage (SAHC) called for ideas from both local and global experts.
Finally, the following repair intervention options were proposed:
Options to restore the Pagoda and the problems they pose
However, more than a decade on, the structure is still in disrepair and its condition is deteriorating by the day. In March 2012, the local government of the county of Yingxian commissioned a project to reduce moisture-induced problems by replacing rotten tiles and fixing the cracks in the building. To a certain extent, this protects the building from problems like erosion due to rain and snow loads and leakage through the dilapidated roof.
The authorities in China say that once the pagoda makes it to UNESCO’s list of protected World Heritage relics, swift measures will be taken towards restoration as there will be enough funds to carry out the necessary measures. In a situation which involves the preservation and restoration of a structure with such a glorious heritage and something so vital to the Chinese identity, it should be of prime importance that the repair interventions be carried out as soon as possible. But with financial and bureaucratic issues, one has to wait and watch what becomes of the Yingxian Pagoda and just hope for the best.
References and further reading:
“STRUCTURAL PERFORMANCE OF DOU-GONG BRACKETS OF YINGXIAN WOOD PAGODA UNDER VERTICAL LOADING” – Enchun Zhu, Zhiyong Chen, Jinglong Pan, Frank Lam
“EXAMPLE OF TRADITIONAL TALL TIMBER BUILDINGS IN CHINA – THE YINGXIAN PAGODA” – Frank Lam, Minjuan He, Chichao Yao
In films and photographs of China and Japan, you’ve seen the striking multi-storied structures known as pagodas. While these familiar towers are the foremost representations of Asian architecture, you may be unaware that they serve as Buddhist monuments, marking the burial site of a Buddhist relic or the tomb of a monk.The pagoda, or ta in Chinese, made its first appearance in China about 68 A.D. when Buddhism arrived from India. As the religion spread during the sixth century, from China to Japan and Korea, the pagoda became a defining form in religious architecture.A towering structure of superimposed stories with overhanging roofs, the pagoda generally is built up from a square, circular, or polygon-shaped foundation. Its origin stems from merging the ancient Indian stupa (the “heap” of brick and stone stacked on the surface of a tomb) with the traditional Chinese multi-storied tower, whch was constructed of timber and topped with a spire.Over the centuries, the design details of the pagoda have evolved and its use has been adapted in Western cultures (often for commercial structures), but its basic shape and its function as a memorial have remained constant in Asia.
Pagodas constitute a special branch of Chinese architecture. They originally served religious purposes, but gradually became more civilian in nature.
Different from the more typical low-rise buildings, pagodas were first popularized in ancient China. They provided people with spectacular views and often featured in Chinese poems.
Below we describe briefly the top 10 time-honored classic pagodas in China, for your reference.
1. Wooden Pagoda of Ying County
In China, this is known as the Yingxian wooden pagoda. It is the oldest and tallest all-wooden pagoda in the world. It was built in 1056 and served as a Buddhist temple.
It’s a 9-storey pagoda 67.3 meters tall, and 30.3 meters in diameter at the bottom, with an octagonal floor plan. It is constructed with wood, without any nails.
54 different kinds of dougong (斗拱，a unique Chinese structure of interlocking beams and crossbeams) were applied in the building, providing architects with some interesting research.
2. Giant Wild Goose Pagoda
The Giant Wild Goose Pagoda, also known as the Big Wild Goose Pagoda, in the Da Ci’en Temple (mercy and kindness temple) complex in Xi’an, is one of the most famous Buddhist pagodas in China, but built with brick.
Dating from 652 AD during the Tang dynasty, it was first built for storing sutras and housing translators of Buddhist classics.
Due to age-induced decay, it has undergone several refurbishments. Today, the pagoda still maintains its original shape after reconstruction during the Ming dynasty. It has 7-storeys and is 64 meters tall.
3. The Iron Pagoda of Yougou Temple, Kaifeng
The Iron Pagoda in Kaifeng, Henan Province was built in 1049 during the Song dynasty. It is also a Buddhist pagoda, with Song-dynasty style; brick-made with glazed tiles.
The “iron” pagoda was not made of iron but brick. Its name became popular during the Yuan dynasty (1271-1368), because its color and sturdiness makes it look like iron.
With 13-storeys, it’s an octagonal-based structure at a height of 55.9 meters. The Iron Pagoda with its densely stacked multiple storeys looks taller than the Yingxian Wooden Pagoda (at 67.3 meters).
4. Three Pagodas of Chongsheng Monastery
Located 1.5 km northwest of Dali old town, the Three Pagodas of Chongsheng Monastery are three independent pagodas which form a symmetric triangle. They are also known as the Dali White Pagodas, since they are all covered with white mud.
The middle one, also known as the Qianxun Pagoda (千寻塔), is the oldest and tallest, built about 1,150 years ago. The other two were built only about 100 years ago.
The Three Pagodas are renowned in Dali for their antiquity, size and well-preserved state.
5. Leifeng Pagoda
Leifeng Pagoda is at the north of West Lake, Hangzhou. Most Chinese people know about it because of the Legend of White Snake, a famous Chinese folk tale.
The original pagoda was built in 975 AD. It’s an octagonal, five-storey structure built of brick and wood. During the Ming dynasty (1368-1644), the pagoda was attacked and its wooden structure was burned.
After that, the remaining brick skeleton fell into decay, since people believed its brick could repel illness and competed to steal the bricks. The pagoda eventually collapsed in 1924 due to lack of maintenance.
It was reconstructed in 2001, with a steel and copper structure, but restoring its previous architectural style.
Liuhe Pagoda, literally the Six Harmonies pagoda, was built in 970 during the Song dynasty (960-1127). Located along the Qiantang River, it was originally built to dispel the annual tidal bores of the Qiantang River.
The pagoda stands 59.9 meters tall. Seen from the outside it’s a 13-storey octagonal wooden structure; while from the inside it’s a 7-storey masonry structure. It is one of the best-preserved masonry-timber structure pagodas in China. What’s more, there’s an ancient Chinese pagoda model exhibition hall next to the pagoda.
7. Tiger Hill Pagoda
Located in Suzhou, the Tiger Hill Pagoda is one of the landmarks of Suzhou. The 7-storey pagoda is 48 meters tall, built with brick but in the timber-style of earlier eras. It’s a representative 10th-century brick pagoda in the Yangtze River basin.
The original pagoda was first built in 601; the existing one began construction in 959 and finished in 961. During the Ming dynasty (1368-1644), the pagoda began to lean towards the northwest, due to its foundations. Now it’s known as the “leaning tower of China“.
8. Songyue Pagoda
The Songyue Pagoda is located at Songyue Monastery in Henan Province. It was built in 523 and has a rare dodecagonal shape. It is regarded as the earliest brick-structure pagoda in China still extant.
The pagoda was built with brick at a height of 40 meters, with an adhesive mixture of sticky rice juice and yellow mud.
9. Feihong/Flying Rainbow Pagoda
Feihong Pagoda at Guangsheng Temple in Shanxi Province is the largest and best-preserved glazed Chinese pagoda. Feihong literally means flying rainbow, a name arising from the pagoda’s colorful decoration.
Feihong is 47.6 meters tall, with 13-storeys. It is a masonry structure built using brick in octagonal pavilion style. Its eaves diminish inwardly at each tier. Around the pagoda’s surface are exquisite sculptures and glazed ornaments.
10. Miaoying Temple White Stupa Pagoda
Located in Xicheng District, Beijing, the White Stupa Pagoda is a rare Tibetan Stupa. It was designed and built in 1271 by a Nepalese architect Anigo, during the reign of Genghis Khan (1206-1227).
Standing at a height of 59.9 meters, it is the oldest and tallest Tibetan-style pagoda in China. It is composed of three parts: a 9-meter high Sumeru pedestal-style platform, an inverted bowl-shaped body and a steeple. Lots of diverse collections of Buddhist statuary were found in 1978 during the repairs.
The generate method of Multi-storey Chinese Pagodas
Different structures have been used in the building of pagodas, depending on the building materials. The structure and method of construction of a wooden pagoda are similar to those of a palace, temple, multistoreyed building or pavilion made of wood, i.e., the traditional beam or bracket system. It is usually composed of a frame, rafters, sheathing, eaves and roof. A pagoda made of bricks and stones, like other brick and stone buildings, is constructed by methods such as piling up bricks or stone blocks and making archways. Metal pagodas are made by moulding and casting metals. Though the building materials and methods of construction differ, the basic structure does not change drastically. A pagoda is composed of the following major parts:
Underground Palace
Most ancient buildings in China were built on solid ground. Usually nothing was built underground. The pagoda, however, was unique in having an underground palace, called the dragon palace or the dragon cave. This special structure is not found in other buildings, such as palaces, temples or multistoreyed buildings. It was added to a Buddhist pagoda to preserve Buddhist relics. According to a survey, Buddhist relics were not buried underground in India, but kept inside the pagodas. When the pagoda was introduced to China, it was combined with China’s traditional burial system. Whenever a pagoda was built, an underground palace was constructed first to preserve the relics and other objects to be buried with the dead. This underground palace was similar to the underground palaces of the mausoleums of emperors and kings in ancient China, but it was usually much smaller and contained fewer funerary objects. The most important thing in an underground palace of a pagoda is a stone container with layer upon layer of cases made of stone, gold, silver, jade and other materials. The innermost case contains the Buddhist relics. The funerary objects in the palace may include copies of Buddhist scriptures and statues of Buddha. Underground palaces were usually built of brick and stone in square, hexagonal, octagonal or round shapes. Occasionally such a structure was built inside the pagoda or semiunderground.
In olden times some superstitious people believed that certain pagodas had been built on “sea holes” to prevent sea water from surging out. If the pagoda fell, the place would be submerged by the sea. The myth came from ignorance of the structure of underground palaces. Sometimes when an underground palace became damaged over the years, underground water would seep into it, and people would mistake it for a “sea hole.” Since Liberation in 1949 thorough investigations have been made of the underground palaces in many important pagodas in Beijing, Hebei, Jiangsu, Hubei and other parts of the country.
For a general understanding of underground pagoda palaces in China let’s look at the underground palace of the sarira pagoda at Jingzhi Temple in Dingzhou, Hebei Province. The name of this particular underground palace was the sarira cabinet, which was inscribed on the wall of the palace, located in the middle of the pagoda’s foundation. A stone shaped like a roof, 60 centimeters deep in the ground, was placed on top of a square hole leading down to the underground palace. The palace room is not an exact square, its east wall being 2.2 meters, west wall 2.1 meters, north wall 2.17 meters and south wall 2.2 meters wide. An arched door is on the south wall. The walls, 2.34 meters high, are joined to the ceiling interlocking brackets. All four walls have murals depicting heavenly kings, Indra, Brahma, boys and maidservants. On the north wall characters read “True Relics of Sakyamuni”, and on both sides are paintings of his ten great disciples. The most incredible thing is that the colors of the columns, brackets, beams and murals are as fresh and bright as if new. Such completely fresh mural paintings of the Song Dynasty cannot be found in buildings aboveground.
A great number of cultural relics were also excavated from this underground palace, including gold and silver ware, porcelain, glassware and wood carvings. Since this pagoda was reconstructed during the Song Dynasty and many funerary objects from deteriorated sites of the Sui and Tang dynasties were also buried in the palace, a few gilded bronze cases of the Sui Dynasty and two stone coffins containing relics of the Tang Dynasty were also unearthed. The large stone case in the middle of the underground palace had been in the basement of the Sui Dynasty pagoda and was replaced after the pagoda was reconstructed. The inscriptions on the stone case indicated its contents and date of burial. Inside were three carved gold coffins, four silver pagodas and a lot of gold and silver ware, porcelain, glazed objects, pearls and other relics.
The underground pagoda palaces resulted from combining the Indian system of burying Buddhist relics in pagodas with the traditional Chinese system of tomb burial.
In cleaning out and repairing old pagodas, many underground palaces and Buddhist and cultural relics buried in them were discovered. Objects found in the Iron Pagoda at Ganlu Temple in Zhenjiang and Huqiu Pagoda in Suzhou, Jiangsu Province, Qianshengxiang Pagoda at Yellow Crane Tower in Wuchang, Hubei Province, the Twin Pagodas at Qingshou Temple in Beijing, Wanjin Pagoda in Nong’an, Jilin Province, and Qianxun Pagoda at Chongsheng Temple in Dali, Yunnan Province, have all provided valuable data for the study of underground pagoda palaces.
Base
The base, on top of the underground palace, supports the whole superstructure. In early times most pagodas had relatively low bases. For instance, the two oldest pagodas in China the pagoda at Songyue Temple of the Northern Wei Dynasty and the Four-Door Pagoda in Licheng of the Sui Dynasty both have very simple, low bases made of brick and stone. Some bases are only ten or twenty centimeters high. They soon become indistinct and even unrecognizable from the ground after being damaged over the years. The base of Xuanzang Pagoda at Xingjiao Temple in Xi’an has become so undistinguishable that the pagoda seems to have been built right on the ground. During the Tang Dynasty, in order to make pagodas such as the Big and Small Wild Goose Pagodas in Xi’an look magnificent, huge bases were built under them. Large bases were also added to pavilion-style pagodas during the Tang Dynasty, for example, the Pagoda of Monk Fanzhou in Anyi of Shanxi Province and the Dragon and Tiger Pagoda at Shentong Temple in Licheng near Jinan.
After the Tang Dynasty the pagodas’ substructure developed into two parts by adding a pedestal to the original base. The effect was a loftier and more majestic pagoda. The lower part of the substructure–the platform –is usually low and without much decoration. The pedestal, in contrast, became the most prominent part of the pagoda with gorgeous decorations. In the process of development the pedestal construction of the multi-eaved pagodas of the Liao and Kin dynasties was most out-standing.
This part of the substructure of pagodas from the Liao and Kin dynasties was called the Sumeru pedestal. According to Buddhist literature, Sumeru is the largest mountain in the world and the home of Buddha and bodhisattvas. To call the pedestal of a pagoda by the name of Sumeru meant that it was a most stable foundation. The supports of palaces, temples, statues of Buddha and other objects were also called Sumeru pedestals. At Tianning Temple in Beijing the pedestal of the pagoda is an octagonal structure on a platform of medium height. The pedestal is divided into two levels. On the first level there are six niches on each side with lion heads carved inside. Carved columns separate the niches. On the lower part of the second level there are five small niches, each with a statue of Buddha inside. On the columns between the niches are images of heavenly guardians in relief sculpture. The brackets on the upper part of the pedestal are decorated with finely carved brick banisters. The banisters are joined to the first storey of the pagoda by a lotus-petal capital. The whole Sumeru pedestal is about one fifth the height of the pagoda.
Later, huge and gorgeous pedestals became very common for other types of pagodas. For a Lamaist pagoda the pedestal, as a major part of the entire structure, often makes one third of its total height. The pedestals of pagodas on vajrasanas, the bulk of the structure, are much bigger than the small pagodas on top of them. Pagodas across streets also have pedestals higher than the pagodas they support. Adopting large pedestals in pagoda construction is closely connected with the traditional Chinese architecture, which always sets great store by the role of base platforms. A large base platform not only provides the building above with a solid and firm foundation but also makes it look majestic and powerful.
Body
The body, or main part, of a pagoda varies depending on the style of architecture. The classification of pagodas was based on the style of the body of the pagoda. Since we have already discussed the outer forms and structures of the pagoda, we are going to concentrate on the inner structure of the pagoda body.
A pagoda may be solid or hollow. Solid pagodas are filled with bricks, stones or rammed earth. Occasionally, a wooden framework is installed inside a solid pagoda to strengthen the bearing capacity of outreaching parts of the pagoda. On the whole, however, the inner structure of a solid pagoda is relatively simple. The following section will focus on hollow pagodas.
1. Wooden pagodas. Wooden pagodas of many storeys were popular during the later years of the Han Dynasty and the Wei, Jin and Northern and Southern dynasties. Most of them have four sides. From historical accounts and existing examples in Japan we have learned that wooden pagodas of this type were composed of the following parts–columns around each level of the pagoda, three rooms on each of the four sides on each level, beams and brackets on the capital of the columns to join with the upper storey, and verandas with banisters around each storey. Eaves stretch out above each of the storeys. As in other multistoreyed buildings, there are stairs for people to climb up and down.
The wooden pagoda in Yingxian County, Shanxi Province, is the best preserved of its kind in China today. It has five levels of eaves on the exterior and five levels of balconies, but there are also five mezzanines in between the main storeys, making it a ten-storey building. The pagoda is octagonal with three rooms and four columns on each side of each exterior storeyed, and the landing are quite spacious. The balconies have protecting banisters so that people can walk around the pagoda freely and enjoy the view. In the middle of the pagoda a huge statue of Buddha was installed. In order to strengthen the structure, double-layer walls were built with post trusses and struts in between to prop up the framework. Spiral stairs lead to each level. Since the pagoda is such a huge and complex structure, the components vary greatly in size and form. For instance, there are more than sixty different kinds of brackets. However, the method of construction was the same as for other wooden buildings.
2. Pagodas with brick exteriors and wooden interiors. The brick walls form the body of the pagoda like a hollow tube, so it is also called a tube-style structure. This structure was used in the construction of both multistoreyed and multi-eaved pagodas during early periods. According to the design for the height of each storey and the positions of doors and windows, holes were left when the brick walls were built for placing the floor slabs and putting up door and window frames. Sometimes pillars were erected at the corners to support the floor above. In most cases spiral stairs were built along the walls.
The number of storeys in a pagoda of this type usually corresponded to the positions of doors and windows and levels of eaves on the outside, and people could ascend them to enjoy the view around. The Big Wild Goose Pagoda in Xi’an, Gongchen Pagoda at Lin’an near Hangzhou and the Twin Pagodas at Luohanyuan Temple in Suzhou are examples of this category. The actual number of storeys in a multi-eaved pagoda, however, usually did not correspond to the positions of doors, windows and eaves, because the eaves were built so close to each other above ground level that there was not enough space for a complete storey in the interior. The pagoda at Songyue Temple, the Small Wild Goose Pagoda and Qianxun Pagoda at Dali’s Chongsheng Temple are typical of this category.
3. Pagodas with a central wooden pillar. Most early wooden pagodas had a central pillar as the mainstay of the structure. A huge pillar, erected right in the middle of the pagoda, propped up the frame from the ground to the top. Descriptions of this construction have been found in historical accounts. A five-storeyed pagoda at Falong Temple in Japan is an existing example of this type. The central pillar helps stabilize the structure. The only extant example of this type in China is the wooden pagoda at Tianning Temple in Zhengding. Since the pagoda is a mixture of wood and brick, the pillar was erected in the upper half of the pagoda, not on the bottom floor, but the central-pillar structure is quite obvious. It is a valuable example in the study of this type of pagoda.
4. Pagodas made of both wood and brick. This type of pagoda was a transition from wooden pagodas to pagodas made of bricks and stones. The body of the pagoda was made of bricks; the eaves, verandas and banisters were made of timber. Wooden columns, beams and eaves were joined to the brick walls for interior framework. This structure was popular during the Song Dynasty. The square pagoda at Songjiang in Shanghai, the Pagoda of Six Harmonies in Hangzhou, Ruiguang Pagoda and Beisi Pagoda in Suzhou are typical of this type.
5. Pagodas with a brick pillar as the mainstay. These were products of China’s traditional brick and stone architecture at its highest development. The main body of the pagoda is completely brick. The stairs, floors, verandas and eaves are all built of brick or stone as integral parts of a complex whole. In the middle of the pagoda a huge brick pillar props up the roof. Every floor level is connected to the central pillar and the walls to form an integrated whole. The floors are built by means of arch bonding and stacking bricks around the central pillar. There are two forms of stairs: One is built along the walls of the central pillar in a “z’ shape; the other winds through the hollow space in the central pillar. In the former case there is a landing around the pillar on every level. Examples of the first structure include the pagoda at Youguo Temple in Kaifeng, Henan Province, the pagoda at Lingyun Temple in Leshan, Sichuan Province, and the one at Famen Temple in Fufeng, Shaanxi Province. The second form is represented by Baodingshan Pagoda in Dazu, Sichuan Province, Liaodi Pagoda at Kaiyuan Temple in Dingzhou and the sarira pagoda in Jingxian County, Hebei Province. Most were built during the Song and Ming dynasties and reached advanced levels in brick and stone architecture.
6. Pagodas build on high platforms. The vajrasanastyle pagodas are pagodas with a huge platform as the main body. Brick or stone staircases were built inside the hollow platform for people to ascend the building. In the pedestal under the pagoda at Zhenjue Temple in Beijing there is a central pillar, and the room around it has a vault roof that serves as the exterior terrace on which small pagodas were erected. The pagodas at Beijing’s Biyun Temple and Hohhot’s Cideng Temple were both built in this style. Some other pagodas have staircases on the outside of the platforms, such as Qingjinhuayu Pagoda in Beijing’s Xihuang Temple and the pagoda at Yuanzhao Temple on Mount Wutai in Shanxi Province.
7. Other types of pagodas. The Lamaist pagoda, for instance, has a round, inverted-bowl-shaped body. During the Ming and Qing dynasties a recess called the yanguang gate was built on the front of the round structure. Sometimes a wooden framework was installed inside the inverted-bowl body to strengthen its stability. Sometimes the inverted-bowl style was combined with a multistoreyed pagoda, such as building a multistoreyed pagoda on top of an inverted-bowl structure, or with a tube-shaped pagoda, or others.
Steeple
Every pagoda is surmounted by a steeple, sometimes pointed and sometimes ball-shaped. They vary greatly in style and building materials. The most commonly used building materials for steeples are bricks, stones and metals.
The steeple, as the tallest part of the pagoda, is extremely important. In Chinese it is called cha, meaning land or territory representing “the country of Buddha.” Therefore, a Buddhist temple is also called cha in China. The lake to the north of Beihai Park in Beijing is called Shi Cha Hai, meaning the Lake of Ten Temples, because there used to be ten great Buddhist temples by the lake.
The steeple is also very important in the architectural structure, because it is the tip of the building. No matter whether the pagoda’s roof is square, hexagonal, octagonal or round, the rafters, sheathing and tile ridges all come to one point, where a component should be fixed to stabilize the roof structure and prevent rain from leaking into the building. The steeple performs these functions.
From the aesthetic point of view, the steeple, surmounting the whole structure of the pagoda, was the crowning image of the building. Therefore, great efforts were made to create a steeple that was exquisite, lofty and graceful.
Early stupas in India also had steeples, but they were not so tall and complex. For instance, a famous Indian stupa built around the first century has only a spire and three layers of umbrella-shaped decorations. After stupas were introduced to China, however, and combined with traditional architectural styles, the steeple of the pagoda, as the emblem of Buddhism, became more and more important and conspicuous. In Stories About Buddhist Temples in Luoyang the steeple of the pagoda at Yongning Temple was said to be as tall as “ten zhang” (33 meters), which may be an exaggeration, but it must have been quite tall. The decorative precious bottle on top of the steeple allegedly could hold 25 dan (2,500 liters) of grain. We can imagine how big it was. Below the precious golden bottle there were thirty tiers of gilded dew basins and many golden bells hanging around them. Since the steeple was very tall, four iron chains linked the steeple with the four comers of the pagoda roof to stabilize the structure. The iron chains were also ornamented with little golden bells.
Many pagoda steeples were built like small Lamaist dagobas. A typical example is the pagoda at Tianning Temple in Anyang, Henan Province. The five-storeyed pagoda is surmounted by a smaller Lamaist dagoba. In Miaoying Temple in Beijing the White Dagoba is composed of a small Lamaist dagoba on top of a larger dagoba. Some Buddhist scriptures say that Buddhist relics are placed in the tip of a pagoda steeple, but no such case has ever been discovered. Researchers believe this was a mistake and that the bottom of the steeple was intended.
The steeple of a pagoda is itself a small dagoba, composed of bottom, body and top with a pole in the middle. Sometimes there is a small cabinet at the bottom of the steeple to hold Buddhist relics, Buddhist sutras or gold, silver, jade and other valuable objects. Such hiding places were found in recent years when repairing old pagodas. At Qianxun Pagoda at Chongsheng Temple in Dali, Yunnan Province, Buddhist relics, scriptures and statues of Buddha were found in a hiding place at the bottom of the pagoda’s steeple, while nothing was found in the underground palace of the pagoda. Whether the underground palace had been robbed of its treasure or it was a mere symbolic form when the real relics and funerary objects had been hidden in the steeple remains an open question.
The base of the steeple was built on the roof of the pagoda, pressing on the rafters, sheathing, corner columns and tile ridges, with the steeple pole planted right in the middle. Steeple bases varied from one another; most were shaped like the Sumeru pedestal, or blooming lotus petals. Some were just plain square platforms. Many had carved patterns of lotus petals or honeysuckle leaves.
The most outstanding characteristic of the steeple was the discs around the pole of the steeple. They were called xianglun (wheel or disc) or golden basins or dew basins, as a symbol of honor or respect for the Buddha. Generally, the bigger the pagoda, the more and bigger the discs. In the early period there were no regulations as to the number of such discs on a particular pagoda. Some had as many as several dozen; others had three or five. Originally, the great wooden pagoda at Yongning Temple ha Luoyang, for instance, had thirty tiers of discs. The Four-Door Pagoda has five and Songyue Temple Pagoda has seven. In later times pagodas were built with one, three, five, seven, nine, eleven or thirteen discs. Most Lamaist dagobas have thirteen discs, which are therefore called “thirteen skies.” An umbrellalike canopy is usually built above the discs as part of the pagoda’s ornaments.
The top of the steeple is also the top of the pagoda. It was usually put above the canopy and consisted of a crescent moon and a precious bead. Sometimes the bead was put above or in the middle of a flame ornament. To avoid any indication of fire, the flame-shaped ornament was called “water smoke.”
The pole of the steeple was the central axle. All the components of a metal steeple were fastened to the pole, which supported the different parts of the steeple. Even small brick pagodas had a wooden or metal pole in the middle of the steeple. According to Buddhist literature, the pole was also called chazhu (steeple pillar) or jincha (golden steeple) or biaocha (symbolic steeple). It was usually made of wood or iron and placed on the roof of the pagoda.
These were the most representative steeple structures. Changes were made in different eras, areas and on different types of pagodas built of different materials. For instance, sometimes three, five, seven or nine metal balls were part of the spire of a pagoda, as in the Twin Pagodas of Chongxing Temple in Beizhen, Liaoning Province. Sometimes a huge canopy was put on top of the pagoda’s steeple, as in the Tianning Temple Pagoda in Beijing. The canopies had different shapes–round, square or octagonal. The spire of Haibao Pagoda in Yinchuan consisted of an onion-shaped ornament, possibly influenced by Islamic architecture. Guang Pagoda at Huaisheng Temple in Guangzhou is unique, since the steeple is a weather vane, completely different from an ordinary Buddhist pagoda.
In search of gojunoto, the five element Japanese pagoda
Structural performance of Dou-Gong brackets of Yingxian Wood Pagoda under vertical load – An experimental study
Zhiyong Chen a b c, Enchun Zhu a b, Frank Lam d, Jinglong Pan a b a Key Lab of Structures Dynamic Behaviour and Control (Harbin Institute of Technology), Ministry of Education, Harbin 150090, China b School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China c Faculty of Forestry and Environmental Management, University of New Brunswick, Fredericton E3B 5A3, Canada d Department of Wood Science, University of British Columbia, Vancouver V6T 1Z4, Canada
Received 17 August 2013, Revised 12 June 2014, Accepted 9 September 2014, Available online 27 September 2014.
Engineering Structures Volume 80, 1 December 2014, Pages 274-288
Source: The Stars Above Us: Regular and Uniform Polytopes up to Four Dimensions
Source: The History of Mathematics From the Egyptians to Archimedes
Source: Platonic Solids, or, the power of counting
Key Terms
Prapanch (Five Fold)
Panch (Five)
5 Platonic Solids
14 Archimedean Solids
Catalan Solids
Regular Convex Polyhedra
Semi Regular Convex Polyhedra
Kepler-Poinsot Polyhedra
4D Polytopes
Five Elements
5 Kosh (Sheaths)
14 Lok (Levels, Realms)
7 Upper Worlds
7 Under Worlds
7 Chakras
5 Continents
7 Seas
Hierarchy Theory
Mount Meru
Nested Platonic Solids
Soccer Ball Geometry
Uniform Polyhedra
Johnson Solids
Goldberg Polyhedra
Albrechet Durer
Leonardo da Vinci
Johannes Kepler
Fra Luca Bartolomeo de Pacioli (ca.1447–1517)
Buckminster Fuller
Fullerenes
Virus Geometry
Symmetry
Polygons
Max Brückner
H.S.M. Coxeter
George W. Hart
Five Platonic Solids
Five Platonic Solids
Tetrahedron
Octahedron
Cube
Icosahedron
Dodecahedron
Five Elements
Fire – Tetrahedron
Air – Octahedron
Earth – Cube
Space – Dodecahedron
Water – Icosahedron
Five Sense Organs
Tongue -Taste – Water
Eyes – Form – Fire
Ears – Sound – Space
Nose – Smell – Earth
Skin – Touch – Air
Five Senses
Hearing
Sight
Touch
Taste
Smell
Source: Polyhedra: Plato, Archimedes, Euler
Source: Polyhedra: Plato, Archimedes, Euler
Source: Polyhedra: Plato, Archimedes, Euler
Source: Sacred Geometry and the Platonic Solids
Source: Sacred Geometry and the Platonic Solids
Source: The Platonic solids and fundamental tests of quantum mechanics
Source: The Platonic solids and fundamental tests of quantum mechanics
Source: The Platonic solids and fundamental tests of quantum mechanics
Source: Vertex Configurations: Platonic Solids, Archimedean Solids, And Johnson Solids
Source: Platonic Solids (Regular polytopes in 3D)
Source: Platonic Solids (Regular polytopes in 3D)
Source: Platonic Solids (Regular polytopes in 3D)
Source: Platonic Solids (Regular polytopes in 3D)
14 Archimedean Solids
Rhombicuboctahedron
Rhombicosidodecahedron
Cuboctahedron
Icosidodecahedron
Truncated Tetrahedron
Truncated Cube
Truncated Octahedron
Truncated Dodecahedron
Truncated Icosahedron
Truncated Cuboctahedron
Truncated Icosidodecahedron
Snub Cube
Snub Dodecahedron
Pseudorhombicuboctahedron ?
Source: Polyhedra: Plato, Archimedes, Euler
Source: Vertex Configurations: Platonic Solids, Archimedean Solids, And Johnson Solids
Source: Vertex Configurations: Platonic Solids, Archimedean Solids, And Johnson Solids
Source: The Stars Above Us: Regular and Uniform Polytopes up to Four Dimensions
Catalan Solids
Source: Catalan Solids
Kepler-Poinsot Solid
Source: Kepler Poinsot Solids
Source: The Stars Above Us: Regular and Uniform Polytopes up to Four Dimensions
Johnson Solids
Source: Johnson Solid
Source: Vertex Configurations: Platonic Solids, Archimedean Solids, And Johnson Solids
Source: Vertex Configurations: Platonic Solids, Archimedean Solids, And Johnson Solids
Source: Max Brücknerʼs Wunderkammer of Paper Polyhedra
Source: Max Brücknerʼs Wunderkammer of Paper Polyhedra
Platonic Solids and Plato’s Theory of Everything
Source: Platonic Solids and Plato’s Theory of Everything
The Socratic tradition was not particularly congenial to mathematics, as may be gathered from Socrates’ inability to convince himself that 1 plus 1 equals 2, but it seems that his student Plato gained an appreciation for mathematics after a series of conversations with his friend Archytas in 388 BC. One of the things that most caught Plato’s imagination was the existence and uniqueness of what are now called the five “Platonic solids”. It’s uncertain who first described all five of these shapes – it may have been the early Pythagoreans – but some sources (including Euclid) indicate that Theaetetus (another friend of Plato’s) wrote the first complete account of the five regular solids. Presumably this formed the basis of the constructions of the Platonic solids that constitute the concluding Book XIII of Euclid’s Elements. In any case, Plato was mightily impressed by these five definite shapes that constitute the only perfectly symmetrical arrangements of a set of (non-planar) points in space, and late in life he expounded a complete “theory of everything”, in the treatise called Timaeus, based explicitly on these five solids. Interestingly, almost 2000 years later, Johannes Kepler was similarly fascinated by these five shapes, and developed his own cosmology from them.
To achieve perfect symmetry between the vertices, it’s clear that each face of a regular polyhedron must be a regular polygon, and all the faces must be identical. So, Theaetetus first considered what solids could be constructed with only equilateral triangle faces. If only two triangles meet at a vertex, they must obviously be co-planar, so to make a solid we must have at least three triangles meeting at each vertex. Obviously when we have arranged three equilateral triangles in this way, their bases form another equilateral triangle, so we have a completely symmetrical solid figure with four faces, called the tetrahedron, illustrated below.
On the other hand, if we make four triangles meet at a vertex, we produce a square-bottomed pyramid, and we can obviously put two of these together, base to base, to give a completely symmetrical arrangement of eight triangular faces, called the octahedron, shown below.
Next, we can make five equilateral triangles meet at a point. It’s less obvious in this case, but if we continue this pattern, adding equilateral triangles so that five meet at each vertex, we arrive at a complete solid with 20 triangular faces. This is called the icosahedron, shown below.
Now, we might try putting six equilateral triangles together at a point, but the result is a planar arrangement of triangles, so it doesn’t give a finite solid. I suppose we could regard this as a Platonic solid with an infinite radius, which might have been useful in Plato’s cosmology, but it doesn’t seem to have been viewed this way. Perhaps this is not surprising, considering the well-known aversion of the ancient Greek mathematicians to the complete infinity. In any case, we clearly can’t construct any more perfectly symmetrical solids with equilateral triangle faces, so we must turn to other possible face shapes.
The next regular polygon shape is the square, and again we find that putting just two squares together does not yield a solid angle, so we need at least three squares to meet at each vertex. Putting three squares together we see that we can add three more to give the perfect solid with six faces, called the hexahedron (also known as the cube). This is shown below.
If we try to make four square faces meet at each vertex, we have another plane surface (giving another “infinite Platonic solid”), so clearly this is the only finite perfectly symmetrical solid with square faces.
Proceeding to pentagonal (five-sided) faces, we find that if we put together 12 pentagons so that three meet at each vertex, we arrive at the fifth Platonic solid, called the dodecahedron, illustrated below.
It isn’t self-evident that 12 identical regular pentagons would come together perfectly like this to form a closed solid, but it works, as Theaetetus proved and as Euclid demonstrates at the conclusion of The Elements. Of course, if we accept that the icosahedron works, then the dodecahedron automatically follows, because these two shapes are “duals” of each other. This means that the icosahedron has 20 faces and 12 vertices, whereas the dodecahedron has 12 faces and 20 vertices, and the angular positions of the face centers of one match up with the positions of the vertices of the other. Thus, once we have the icosahedron, we can just put a dot in the center of each face, connect the dots, and viola!, we have a dodecahedron. Similarly, the cube and the octahedron are duals of each other. Also, the tetrahedron is the dual of itself (so to speak).
Clearly it’s impossible for four (or more) pentagonal faces to meet at a vertex, because they subtend more than 360 degrees. For hexagonal (six-sided) faces, three hexagons meeting at a point constitute another “infinite solid”, i.e., a planar surface. It’s also obvious that no higher-order polygon can yield a solid, so the five solids already mentioned – tetrahedron, hexahedron, octahedron, icosahedron, and dodecahedron – are the only regular polyhedrons. Theaetetus not only proved that these solids exist, and that they are the only perfectly symmetrical solids, he also gave the actual ratios of the edge lengths E to the diameters D of the circumscribing spheres for each of these solids. This is summarized in Propositions 13 through 17 of Euclid’s Elements.
In Timaeus, Plato actually chose to constitute each of these solids from right triangles, which played the role of the “sub-atomic particles” in his theory of everything. In turn, these triangular particles consisted of the three legs (which we might liken to quarks), but these legs were ordinarily never separated. The right triangles that he chose as his basis particles were of two types. One is the “1,1,” isosceles triangle formed by cutting a square in half, and the other is the “1,2,” triangle formed by cutting an equilateral triangle in half. He used these to construct the faces of the first four solids, but oddly enough he didn’t just put two together, he used six “1,2, triangles to make a triangular face, and four “1,1,” triangles to make a square face, as shown below.
Of course, it’s not possible to build a pentagon from these two basic kinds of right triangles, and Plato doesn’t actually elaborate on how the faces of the dodecahedron are to be constructed, but from other sources we know that he thought each face should be composed of 30 right triangles, probably as shown on the right-hand figure above, so that the dodecahedron consisted of 360 triangles. The tetrahedron, octahedron, and icosahedron consisted of 24, 48, and 120 triangles (of the type 1,2,), respectively, and the hexahedron consisted of 24 triangles (of the type 1,1,).
Now, if the basic triangles were the subatomic particles, Plato regarded the solids as the “atoms” or corpuscles of the various forms of substance. In particular, he made the following identifications
The idea that all the constituents of nature consist of mixtures of a small number of “elements”, and in particular the selection of the four elements of earth, water, air, and fire, is attributed to an earlier Greek philosopher Empedocles of Agrigentum (495-435 BC). Empedocles believed that although these elements (which he called “the roots of all things”) could be mixed together in various proportions, the elements themselves were inviolable, and could never be changed. In contrast, one of the intriguing aspects of Plato’s theory was that he believed it was possible for the subatomic particles to split up and re-combine into other kinds of atoms. For example, he believed that a corpuscle of liquid, consisting of 120 “type 1” triangles, could be broken up into five corpuscles of plasma, or into two corpuscles of gas and one of plasma. Also, he believed that the “smaller” corpuscles could merge into larger corpuscles, so that (for example) two atoms of plasma could merge and form a single atom of gas. However, since the basic triangles making up “earth” (cubes) are dissimilar to those of the other forms of substance, he held that the triangles comprising cubes cannot be combined into any of the other shapes. If a particle of earth happened to be broken up into its constituent triangles, they will “drift about – whether the breaking up within fire itself, or within a mass of air or water – until its parts meet again somewhere, refit themselves together and become earth again”.
When Plato asserts that the [1,1,] triangles cannot combine into anything other than a cube, it’s conceivable that he was basing this on something more that just the geometric dissimilarity between this triangle and the [1,2,] triangle. He might also have had in mind some notion of the incommensurability of the magnitudes and , not only with the unit 1, but with each other. Indeed the same Theaetetus who gave the first complete account of the five “Platonic” solids is also remembered for recognizing the general fact that the square root of any non-square integer is irrational, which is to say, incommensurable with the unit 1. It isn’t clear whether Theaetetus (or Plato) knew that two square roots such as and are also incommensurable with each other, but Karl Popper (in his anti-Plato polemic “The Free Society and its Enemies”) speculated that this might have been known, and that Plato’s choice of these two triangles as the basic components of his theory was an attempt to provide a basis (in the mathematical sense) for all possible numbers. In other words, Popper’s idea is that Plato tentatively thought the numbers 1, , and are all mutually incommensurable, but that it might be possible to construct all other numbers, including , π, etc., as rational functions of these.
Of course, Book X of Euclid’s Elements (cf. Prop 42) dashes this hope, but it’s possible that the propositions recorded there were developed subsequent to Plato’s time. Popper also makes much of the numerical coincidence that + is approximately equal to π, and speculates that Plato might have thought these numbers were exactly equal, but this doesn’t seem credible to me. For one thing, it would give a means of squaring the circle, which would certainly have been mentioned if anyone had believed it. More importantly, the basic insight of Theaetetus was in recognizing the symmetry of all the infinitely many irrational square roots, and it just doesn’t seem likely that he (or Plato) would have been misled into supposing that just two of them (along with the unit 1) could form the basis for all the others. It’s a very unnatural idea, one that would not be likely to occur to a mathematician. (Still, an imaginative interpreter could probably discern correspondences between the four basis vectors of “The Platonic Field“, i.e., numbers of the form A + B+ C + D and Plato’s four elements, not to mention the components of Hamilton’s quaternions.)
It’s also interesting that Plato describes the “1,1,” triangle as the most “stable”, and the most likely to hold its shape, thus accounting for the inert and unchanging quality of the solid elements. He didn’t elaborate on his criterion for “stability”, although we can imagine that he had in mind the more nearly equal lengths of the edges, being closer to equilibrium. On the other hand, this would suggest that the equilateral triangle (which is the face of Plato’s “less stable” elements) was highly stable. Plato made no mention of the fact that the cube is actually the only unstable Platonic solid, in the sense of rigidity of its edge structure. In addition, the cube is the only Platonic solid that is not an equilibrium configuration for its vertices on the surface of a sphere with respect to an inverse-square repulsion. Nevertheless, the idea of stability of the sub-atomic structure of solid is somewhat akin to modern accounts of the stability of inert elements.
We can also discern echoes of Plato’s descriptions in Isaac Newton’s corpuscular theory. Newton’s comments about the “sides” of light particles are very reminiscent of Plato’s language in Timaeus. It’s also interesting to compare some passages in Timaeus, such as
And so all these things were taken in hand, their natures being determined by necessity in the way we’ve described, by the craftsman of the most perfect and excellent among things that come to be…
with phrases in Newton’s Principia, such as
…All the diversity of created things, each in its place and time, could only have arisen from the ideas and the will of a necessarily existing being…
…all phenomena may depend on certain forces by which the particles of bodies…either are impelled toward one another and cohere in regular figures, or are repelled from one another and recede…
…if anyone could work with perfect exactness, he would be the most perfect mechanic of all…
Plato explicitly addressed the role of necessity in the design of the universe (so well exemplified by the five and only five Platonic solids), much as Einstein always said that what really interested him was whether God had any choice in the creation of the world. But Plato was not naive. He wrote
Although [God] did make use of the relevant auxiliary causes, it was he himself who gave their fair design to all that comes to be. That is why we must distinguish two forms of cause, the divine and the necessary. First, the divine, for which we must search in all things if we are to gain a life of happiness to the extent that our nature allows, and second, the necessary, for which we must search for the sake of the divine. Our reason is that without the necessary, those other objects, about which we are serious, cannot on their own be discerned, and hence cannot be comprehended or partaken of in any other way.
The fifth element, i.e., the quintessence, according to Plato was identified with the dodecahedron. He says simply “God used this solid for the whole universe, embroidering figures on it”. So, I suppose it’s a good thing that the right triangles comprising this quintessence are incommensurate with those of the other four elements, since we certainly wouldn’t want the quintessence of the universe to start transmuting into the baser substances contained within itself!
Timaeus contains a very detailed discussion of virtually all aspects of physical existence, including biology, cosmology, geography, chemistry, physics, psychological perceptions, etc., all expressed in terms of these four basic elements and their transmutations from one into another by means of the constituent triangles being broken apart and re-assembled into other forms. Overall it’s a very interesting and impressive theory, and strikingly similar in its combinatorial (and numerological) aspects to some modern speculative “theories of everything”, as well as expressing ideas that have obvious counterparts in the modern theory of chemistry and the period table of elements, and so on.
Timaeus concludes
And so now we may say that our account of the universe has reached its conclusion. This world of ours has received and teems with living things, mortal and immortal. A visible living thing containing visible things, and a perceptible God, the image of the intelligible Living Thing. Its grandness, goodness, beauty and perfection are unexcelled. Our one universe, indeed, the only one of its kind, has come to be.
The speculative details of Plato’s “account of the universe” are not very satisfactory from the modern point of view, but there’s no doubt that – at least in its scope and ambition as an attempt to represent “all that is” in terms of a small number of simple mathematical operations – Plato’s “theory of everything” left a lasting impression on Western science.
Source: Platonic Solids, or, the power of counting
Six (6) 4D Polytopes
Source: 4d-polytopes described by Coxeter diagrams and quaternions
Discovery of the Platonic solids; tetrahedron, cube, octahedron, icosahedron and dodecahedron dates back to the people of Scotland lived 1000 years earlier than the ancient Greeks and the models curved on the stones are now kept in the Ashmolean Museum at Oxford [1]. Plato associated tetrahedron with fire, cube with earth, air with octahedron, and water with icosahedron. Archimedes discovered the semi-regular convex solids and several centuries later they were rediscovered by the renaissance mathematicians. By introducing prisms and anti-prisms as well as four regular non-convex polyhedra, Kepler completed the work in 1620. Nearly two centuries later, in 1865, Catalan constructed the dual solids of the Archimedean solids now known as Catalan solids [2]. Extensions of the platonic solids to 4D dimensions have been made in 1855 by L. Schlaffli [3] and their generalizations to higher dimensions in 1900 by T.Gosset [4]. Further important contributions are made by W. A. Wythoff [5] among many others and in particular by the contemporary mathematicians H.S.M. Coxeter [6] and J.H. Conway [7].
The 3D and 4D convex polytopes single out as compared to the polytopes in higher dimensions. The number of Platonic solids is five in 3D and there exist six regular polytopes in 4D contrary to the higher dimensional cases where there exist only three platonic polytopes which are the generalizations of tetrahedron, octahedron and cube to higher dimensions. The Platonic and Archimedean solids [8] as well as the Catalan solids [9] can be described with the rank-3 Coxeter groupsW(A3),W(B3) and W(H3).
The 4D polytopes are described by the rank-4 Coxeter groups W(A4 ), W(B4 ), W(H4 ) and the group W (F4 ).
Source: The Stars Above Us: Regular and Uniform Polytopes up to Four Dimensions
Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces
Source: Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces
Source: Truncated Truncated Dodecahedron and Truncated Truncated Icosahedron Spaces
Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses
Stan Schein stan.schein@gmail.com and James Maurice Gayed
Edited by Patrick Fowler, The University of Sheffield, Sheffield, United Kingdom, and accepted by the Editorial Board January 7, 2014 (received for review June 10, 2013) February 10, 2014 111 (8) 2920-2925 https://doi.org/10.1073/pnas.1310939111
*Budapest University of Technology and Economics Budapest, Műegyetem rkp. 3., H-1521 Hungary tarnai@ep-mech.me.bme.hu
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Valencia Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures 28 September – 2 October 2009, Universidad Politecnica de Valencia, Spain Alberto DOMINGO and Carlos LAZARO (eds.)
Viewpoints which Matter 
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