Cube of Space letters with six cardinal directions (up, down, east, west, north, south). The verse in chapter 5 associates 12 hebrew letters with either 12 diagonal directional 'arms' or 12 diagonal boundaries (different translations contradict each other), which some interpret as referring to the 12 edges of an octahedron, though Paul Foster Case interpreted these as the 12 edges of a cube. In the most authoritative English translation of the Sepher Yetzirah, scholar Aryeh Kaplan interprets this verse (Chapter 5, Verse 2) as describing a cube. (Sefer Yetzirah Page 203) While occult author Kevin Townley explains a cosmology with an octahedron within
Bhargava cube the edges of the corresponding faces. The integer binary quadratic form associated with this pair of faces is defined as The quadratic form is also defined as However, the former definition will be assumed in the sequel. Let the cube be formed by the integers "a", "b", "c", "d", "e", "f", "g", "h". The pairs of matrices associated with opposite edges are denoted by ("M", "N"), ("M", "N"), and ("M", "N"). The first rows of "M", "M" and "M" are respectively ["a" "b"], ["a" "c"] and ["a" "e"]. The opposite edges in the same face are the second rows. The