It is well-known that the atharva vedic tradition provides the vidhi for one of the great rites of kumAra- the skanda yAga promulgated by gopatha. But known only to a select few, who maintain the continuity with the divyaugha via the mAnavaugha on the kaumAra path the AV provides that most supreme rahasya of skanda – the mahA-mantra with which the manifestation of deva attains completeness. This great mantra is the aShTAkSharI vidyA of the atharvaveda. It is to deployed only by a practitioner of the atharvaNa-shruti, who has been introduced to the rahasya-s of the bhR^igu veda. One who has not sworn his allegiance to the veda of the bhR^igu-a~Ngiras should undergo a new upanayana and study the AV. He then performs oblations to the atharva veda with the two sUktaMs (AV-vulgate edition 19.22 and 19.23) as done by the atharva vedI-s on the upAkarma day, before learning this mantra (AV 20-132.16). This mantra belongs to the khila section found in kANDa 20 of the vulgate text known as the kuntApa hymns that are deployed in the shrauta context during the mahAvrata rituals. The kuntApa-s are all enigmatic hymns that at the face of it make no sense. They are attributed to the bhArgava aitaSha (the aitaSha pralApa), a descendant of aurva. The mantra’s R^iShi is bhR^igu, the Chandas is eka-pada gayatrI and its devatA is skanda.
The key secret of the aShTAkSharI lies in the sampuTIkaraNa with the two ShaDakSharI-s that result in the emanation of the two basic maNDala-s of kArttikeya: the vajra-maNDala and the ghana-maNDala. When the aShTAkSharI is combined with the ShaDakSharI (namaH kumArAya) then it results in the expansion of the planar ShaTkoNa yantra defined by the ShaDakSharI’ syllables occupying the vertices of the yantra into the 3D octahedral vajra-maNDala. Now the 6 syllables of the ShaDakSharI occupy the 6 vertices of the octahedron, while the 8 syllables of the aShTAkSharI occupy the 8 faces of the maNDala.
This symmetry in the saMpuTIkaraNa of the aShTAkSharI and the two ShaDakSharI-s illustrates a geometric relationship of the two polyhedra known as the dual. The dual of a polyhedron A is defined as polyhedron B, which constructed by taking the centers of the faces of the A as the vertices of B. The cube (ghana maNDala) and the octahedron (vajra-maNDala) are duals of each other.