THE OM MANI PADME HUM, THE PLATONIC SOUL, THE TAO, AND THE GREEK CROSS ARE AN ARCHITECTURAL TOOL

The plan of Borobuclur conforms with two concentric octagrams. The lines of the scheme, their lengths, and their intersections, determine the articulation of the Borobudur composition, i. e. the sizes of every part and of the whole as well. The sizes of Borobudur are modular. Their modular multiples are Pell numbers, the ratios of which rationally approximate the irrational proportions in octagram  If Borobudur numbers are located in the Peli number-pattern and connected with a line, the syllable OM, written in Sanskrit, appears. The word octagram is only the modern European name of the symbol of OM. The prayer OM MANI PADME HUM, translated as 'the JEWEL and the LOTOS', is a good description of octagram.

design a town. 9 The Roman architecture is indeed shaped with proportions generated in octagram. 10 As an example, see the plan of Roman Emona,H an Augustean town under the present name of Ljubljana, Yugoslavia (Ill. 5). An analogous Egyptian example is Iklmaton's North Palace (Ill. 6). The Egyptian hieroglyphic niwtsaid to mean »the crossroad of a village« 12 -is a mutation of octagram, meaning the »composition, building<<. 13 The forms in octagram are shaping architectures in Eurasia. In Asia, e. g., see the plan of Peking 14 and of Kyoto 15 (Ill. 7 and Ill. 8). As a Byzantine example, see the Serbian church of Hilandar 15 , on the Athos Peninsula, Greece (Ill. 9). A fine example of Islamic architecture is a mosque of Ottoman type, the Husrev-bey mosque in Sarajevo, Yugoslavia 16 (Ill. 10).
In the Middle Ages, the ociagram as an architectural scheme was called »the Greek Cross«. The early Christian symbol was IHTHYS 17 , but the cross, which is one of the mutations of octagram, soon substituted it. The traces of OM, AUM, AVM, AUNG, in Europe are still evident in the word AM(en) and in the invovation AV(e) M(aria).
The Indian Vastu Purusha mandala, the manduka mandala, and paranzasayika mandala,18 are the modular subdivisions of the octagram's square (Ill. 11). The number of pada, determining the length of the mandala, is a specific Pell term.
The conclusion of my paper is that the scheme of octagram, under which the symbol of OM is known, is shaping the historical architecture of the Old World. It is evident in Egyptian, Roman, Byzantine, Moslem, Hindu, Chinese, Japanese, and Buddhist architectures. Apparently its origin is in Asia.  4. Plato's Soul of the Universe, consisting of the Same, of the Other, and of the third Being, is the octagram's scheme.

NOTES
5. The Roman Emona is in the proportion, called quadriagon. 6. The plan of the North Palace in Tell-El-Amarnah is a quadriagon, rationally approximated with the ratio 5: 4.
7. The plan of Peking is in the octagram's proportions. 8. The plan of Kyoto is in the ratio 7: 6, which is an approximation of quadrzagon.
9. The Byzantine church of Hilandar, Athos, is designed with the aid of an octagram.
10. The Husrev-Bey mosque in Sarajevo, Yugoslavia, is designed with the aid of an octagram.
11. The modular subdivision of Indian architectural mandalas is a combination of the octagram's square and of the Pell numbers.
12. The planning grid for the groundfloor of the church in Bogojina, Slovenia, by Joze Plecnik implies the Greek cross, analogous to the Indian paramasayika mandala or Vastu Purusha mandala (See Ills, 11. and 15.).
14. The Greek Cross on the groundplane of Michelangelo's St. Peter in Rome. 15. The Indian Vastu Purusha mandala, or paramasayika mandala. 16. The metamorphoses of octagram: the Egyptian hieroglyphic NIWT, the early cross in catacombs, the Vitruvian wind-rose. the symbol of Rosy-crucians, the Indian Shri Yantra, the OM Yantra, the Indo-Chinese mandala, the TAO.