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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