The unit here was chosen as the tesseract's square diagonal.

By the very definition of Waterman polytopes, not necessarily all vertices are on the same sphere. However in here both the 8 vertices of the d-scaled hex layer and the other 96 vertices of the (unit) tah layer belong to the same radius.

Incidence matrix according to Dynkin symbol

do3ox3ox4oo&#zh   → height = 0, where d = 3 pseudo
(tegum sum of d-hex and tah)

o.3o.3o.4o.     | 8  * ♦  24  0  0 | 12  24  0  0  0 |  8  6  0
.o3.o3.o4.o     | * 96 |   2  2  2 |  2   4  1  4  1 |  4  2  2
----------------+------+-----------+-----------------+---------
oo3oo3oo4oo&#h  | 1  1 | 192  *  * |  1   2  0  0  0 |  2  1  0  h
.. .x .. ..     | 0  2 |   * 96  * |  1   0  1  2  0 |  2  0  2  x
.. .. .x ..     | 0  2 |   *  * 96 |  0   2  0  2  1 |  2  2  1  x
----------------+------+-----------+-----------------+---------
.. ox .. ..&#h  | 1  2 |   2  1  0 | 96   *  *  *  * |  2  0  0
.. .. ox ..&#h  | 1  2 |   2  0  1 |  * 192  *  *  * |  1  1  0
.o3.x .. ..     | 0  3 |   0  3  0 |  *   * 32  *  * |  0  0  2
.. .x3.x ..     | 0  6 |   0  3  3 |  *   *  * 64  * |  1  0  1
.. .. .x4.o     | 0  4 |   0  0  4 |  *   *  *  * 24 |  0  2  0
----------------+------+-----------+-----------------+---------
.. ox3ox ..&#h  | 1  6 |   6  3  3 |  3   3  0  1  0 | 64  *  *  hippy variant
.. .. ox4oo&#h  | 1  4 |   4  0  4 |  0   4  0  0  1 |  * 48  *  squippy variant
.o3.x3.x ..     | 0 12 |   0 12  6 |  0   0  4  4  0 |  *  * 16  tut