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
Rubik's Cube group define orientation. One choice is the following group, given by generators (the last generator is a 3 cycle on the edges): Since "C" is a normal subgroup and the intersection of "C" and "C" is the identity and their product is the whole cube group, it follows that the cube group "G" is the semi-direct product of these two groups. That is Next we can take a closer look at these two groups. The structure of "C" is since the group of rotations of each corner (resp. edge) cube is formula_30 (resp. formula_31), and in each case all but one