By the very definition of Waterman polytopes, not necessarily all vertices are on the same sphere. However in here both the 64 (Q,x)-sidpith vertices and the 64 (q,x)-tat vertices belong to the same radius.

Incidence matrix according to Dynkin symbol

((Qo3oo3oq4xx))&#zh   → height = 0
                        where Q = sqrt(8) = 2.828427 (pseudo)
(tegum sum of (Q,x)-sidpith with (q,x)-tat)

  o.3o.3o.4o.       | 64  * |  3   3  0  0 |  3   3  3  0 | 1  3  1  0
  .o3.o3.o4.o       |  * 64 |  0   3  3  1 |  0   6  3  3 | 0  3  3  1
--------------------+-------+--------------+--------------+-----------
  .. .. .. x.       |  2  0 | 96   *  *  * |  2   0  1  0 | 1  2  0  0  x
  oo3oo3oo4oo  &#h  |  1  1 |  * 192  *  * |  0   2  1  0 | 0  2  1  0  h
  .. .. .q ..       |  0  2 |  *   * 96  * |  0   2  0  2 | 0  1  2  1  q
  .. .. .. .x       |  0  2 |  *   *  * 32 |  0   0  3  0 | 0  3  0  0  x
--------------------+-------+--------------+--------------+-----------
  .. .. o.4x.       |  4  0 |  4   0  0  0 | 48   *  *  * | 1  1  0  0
  .. .. oq ..  &#h  |  1  2 |  0   2  1  0 |  * 192  *  * | 0  1  1  0
  .. .. .. xx  &#h  |  2  2 |  1   2  0  1 |  *   * 96  * | 0  2  0  0
  .. .o3.q ..       |  0  3 |  0   0  3  0 |  *   *  * 64 | 0  0  1  1
--------------------+-------+--------------+--------------+-----------
  .. o.3o.4x.       |  8  0 | 12   0  0  0 |  6   0  0  0 | 8  *  *  *  x-cube
((Qo .. oq4xx))&#zh |  8  8 |  8  16  4  4 |  2   8  8  0 | * 24  *  *  Qo oq4xx&#zh (squobcu variant)
  .. oo3oq ..  &#h  |  1  3 |  0   3  3  0 |  0   3  0  1 | *  * 64  *  oo3oq&#h (tall tet variant)
  .o3.o3.q ..       |  0  4 |  0   0  6  0 |  0   0  0  4 | *  *  * 16  q-tet