The basic geometry of the kAlAtmaka yantra
The inscription records of Angkor Wat by the French archaeologists points to a rare tantric prayoga of the siddhAnta srotas, whose performance appears to barely survive today in the drAviDA country (perhaps until relatively recently in Nepal). The inscription in question is from the period of the 1300s apparently from the period of the reign of indrajayavarman. The relevant statement from the inscription is:
“tasmin kuru mahad yAgaM yathoktaM pArameshvare … kR^itvAn sa mahad yAgaM kAla-yAgaM iti shrutaM | sarasvatI yAga yutaM loka-pAla-samAvR^itaM ||”
It describes a great yAga which has been laid down in the siddhAnta tantra known as the pArameshvara Agama. This great yAga is known as kAla-yAgaM. In its performance the mantra-vAdin is supposed to include the yAgA of sarasvatI and surround it by that of the loka-pAla-s. So what is this rite being described by the Angkor Wat inscription? An examination of the ritual prayoga-s of the Chidambaram dIkShita-s reveals that it refers to the prayoga of the exalted vyomavyApin mantra. This mantra as per the kAmikAgama is used in the final step of the dIkSha into the siddhAnta srotas along with the mAtR^ikA mantra-s signifying the circle of sarasvatI before it. However, the ritual in question here is the one laid out by the 9th paTala of the guhya section of the archaic nishvAsa tantra. It is also found in the now partially lost pArameshvara tantra, confirming the statement in the Angkor inscription. It is also alluded to in the svAyambhuva sUtra-s as the form of mahAdeva as kAlAtmA (the version edited by Pierre-Sylvain Filliozat may not contain the original reading) commented upon by the great AchArya sadyojyotis. The nishvAsa guhya described the yAga as the worship of shiva as “saMvatsara-sharIriNaH” or with his body as the year. The rite was connected with the construction of the kAlAtman maNDala, which is being implied implicitly by the word yAga in the Angkor inscription (the yAga being the fire rite accompanying the installation and worship of the maNDala). The basic geometry of the mandalA has a dodecagonal plan with 12 spokes leading to the outer rim with petals (circles). On each of these 12 spokes and petals 30 akShara-s of the vyomavyApin mantra were laid out (=360). The remaining 8 akShara of the vyomavyApin were laid on the inner octagonal nave. This was surrounded by a decagonal rim on which were laid, 5 per side, the 50 mAtR^ika-s composing the akShara-svarUpa of sarasvatI (this is clearly mentioned in the pArameshvara). Outside of it the 8 direction was a bhUpura with loka-pAla stationed therein starting with indra. The yAga of mahAdeva in the form of the kAlAtmA (embodied in this maNDala) involved the ritual to the central shiva with the vyomavyApin mantra arranged as a manifestation of the year, to sarasvati in the surrounding mAtR^ika chakra and to the loka-pAla-s in their AvaraNa.
This construction of the maNDala is different from the navanAbha maNDala also constructed based on the vyovyApin mantra. The latter is described by the great Kashmirian tantric bhaTTa rAMakaNTha deshika (rAmakaNTha-II) in his composition known as the vyomavyApin stava. The medieval brAhmaNa vedaj~na (commenting on rAmakaNTha, and following trilochana-shiva) from TiruvATuturai in the Tamil country states that this yantra was first promulgated by the bhArgava R^iShi ruru (Hence, his collection form the tantra of the Urdhva srotas known as raurava) and the vyomavyApin mantra is supposed to have emerged from the IshAna face of shiva. The features of the navanAbha yantra are derived based on the kalottara and mata~Ngaparameshavara texts. This maNDala has a nonagonal symmetry with 40 akShara-s in each of the 9 sectors and 8 arranged in a central nave. The kAlAtman envisages shiva as encompassing time and the navanAbha envisages the deva as encompassing space.
These conceptions of shiva express a continuity with the vedic tradition where rudra is invoked at the end of the piling of the altar in the agnichayana. In the yajur vedic rite rudra is invoked as encompassing space as the 4 cardinal directions and the vertical axis and time in the form of the 5 saMvatsara-s of the vedic 5 year cycle. Amongst these rudra is said to stand like a fierce tiger. Likewise, the mention of the kAla maNDala in the Cambodian inscription, which arranges the vyomavyApin to correspond to the 12*30 day months of the saMvatsara, reminds one of the astronomical constants embedded in the main temple of Angkor Wat. For example, the outline of the base-plan of the upper elevation of the temple has 12 projections and the sum of the lengths of the N-S and E-W axes is 365.37 Cambodian cubits (described in Eleanor Mannikka’s work). While, the main temple of Angkor Wat is one dedicated to viShNu, the basic ideas of maNDala geometry inhere to both siddhAnta and pA~ncharAtra temple constructions. After all the mantra and the yantra are the deity.
The Angkor Wat upper elevation
mAnasa-taraMgiNI 