Acronym | ... |
Name | Waterman polychoron number 5 wrt. primitive tesseractic lattice C4 centered at a lattice point |
Face vector | 64, 312, 352, 104 |
By the very definition of Waterman polytopes, not necessarily all vertices are on the same sphere. In here the 48 maximal ones (q-thex vertices) have a circumradius of sqrt(5) = 2.236068, while the other 16 vertices (u-tes ones) only are at an radius of 2.
Incidence matrix according to Dynkin symbol
oq3oq3oo4uo&#zh → height = 0, where u = 2 (pseudo) (tegum sum of q-thex and u-tes) o.3o.3o.4o. | 16 * | 12 0 0 | 6 12 0 | 4 4 0 u-tes-vertices .o3.o3.o4.o | * 48 | 4 1 4 | 4 8 4 | 4 4 1 q-thex-vertices ----------------+-------+-----------+-----------+-------- oo3oo3oo4oo&#h | 1 1 | 192 * * | 1 2 0 | 2 1 0 h .q .. .. .. | 0 2 | * 24 * | 4 0 0 | 4 0 0 q .. .q .. .. | 0 2 | * * 96 | 0 2 2 | 1 2 1 q ----------------+-------+-----------+-----------+-------- oq .. .. ..&#h | 1 2 | 2 1 0 | 96 * * | 2 0 0 .. oq .. ..&#h | 1 2 | 2 0 1 | * 192 * | 1 1 0 .. .q3.o .. | 0 3 | 0 0 3 | * * 64 | 0 1 1 ----------------+-------+-----------+-----------+-------- oq3oq .. uo&#zh | 2 6 | 12 3 3 | 6 6 0 | 32 * * hexagonal bipyramid .. oq3oo ..&#h | 1 3 | 3 0 3 | 0 3 1 | * 64 * trigonal pyramid .. .q3.o4.o | 0 6 | 0 0 12 | 0 0 8 | * * 8 q-oct
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