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
Partial cube "Hamming labeling"; it represents an isometric embedding of the partial cube into a hypercube. was the first to study isometric embeddings of graphs into hypercubes. The graphs that admit such embeddings were characterized by and , and were later named partial cubes. A separate line of research on the same structures, in the terminology of families of sets rather than of hypercube labelings of graphs, was followed by and , among others. Every tree is a partial cube. For, suppose that a tree "T" has "m" edges, and number these edges (arbitrarily) from 0 to "m" − 1. Choose a