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The 64 permutations are the base 2 expansions of the 27 base 3 permutations. They are identical to the 64 hexagrams of the I Ching although I am sceptical about the concepts traditionally attached to them.
The 64 permutations fit exactly apon the features of the dodecahedron.
For a more detailed report on how the Dodecahedron is intimately related to many areas of esoteric thought check out:
Profound Secrets of the Dodecahedron
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