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PART 1.4: Advanced Geometric Expansion Rates
POSTULATE 4.1: a combined hyper-tetrahedron
& hyper-cube lattice in 4-space.
AXIOM 4.2: a hyper-tetrahedron & hyper-cube,
both at 45° & perigee, form the combined lattice.
LEMMA 4.3: the hyper-tetrahedron is @ perigee
what a stelloctahedron is at apogee or “nested.”
LEMMA 4.4: the hyper-cube is @ 45° what a
tesseract is at perigee, seen from above a corner.
POSTULATE 4.5: the 36 legs of the lattice
formed by a tesseract over-top a stelloctahedron.
LEMMA 4.6: the 22 legs of a hyper-cube lattice
@ 45° perigee: 3 horizontal, 7 vert., 12 diaganol.
LEMMA 4.7: the 12 legs of a hyper-tetrahedron
@ 45° perigee: 2 horizontal, 3 vert., 7 diaganol.
AXIOM 4.8: the 36 legs of the mixed lattices @
45° perigee: 5 horizontal, 11 vert., 20 diaganol.
POSTULATE 4.9: re. the 17 nodes of the lattice
formed by a tesseract over-top a stelloctahedron.
LEMMA 4.10: 10 nodes of hyper-cube lattice @
45° perigee: 4 types: 2X bases-3,5&6, 4X base-4.
LEMMA 4.11: 7 nodes of a stelloctahedron @ 45°
perigee: 2 types: 6X base-3, & 1X base-6.
AXIOM 4.12: 17 nodes of the mixed lattices @
45° perigee: 5 types: 2X base-3&6, 3X base-8,
4X base-4, & 6X base-5.
POSTULATE 4.13: the central 7 nodes of the
lattice of a tesseract over a stelloctahedron.
AXIOM 4.14: 2 stelloctahedron legs over-lap the
central vert., and 3 hyper-cube legs over-lap it.
AXIOM 4.15: 5 legs within 5 nodes besides +
1 leg each for the top- and bottom-most nodes.
AXIOM 4.16: there are 6 vert. legs between the 7
central nodes, as 7 chakras and 64 I Ching hex’s.
AXIOM 4.16: the central 7 nodes also correspond
to the 7 methods of verbal communication, thus:
POSTULATE 4.17: re. the 72 traits of the lattice.
THEOREM 4.18: 3 X 2 = 6; 6 X 2 = 12; 12 X 3 = 36
36 X 5 = 180°; 360° / 5 = 72.
THEOREM 4.19: 22 + 14 = 36; 36 + 14 = 50; 50 +
14 = 64; 64 + 8 = 72.
THEOREM 4.20: 22 + 50 = 36 X 2.