By the very definition of Waterman polytopes, not necessarily all vertices are on the same sphere. However in here both layers of mutually inverted (u,x)-srip clearly belong to the same radius.

Incidence matrix according to Dynkin symbol

((uo3ox3xo3ou))&#zq   → height = 0
                        where u = 2 pseudo

  o.3o.3o.3o.       & | 60 |   4   4 |  2  2  2   6 |  1  3  2
----------------------+----+---------+--------------+---------
  .. .. x. ..       & |  2 | 120   * |  1  1  0   1 |  1  1  1  x
  oo3oo3oo3oo  &#q    |  2 |   * 120 |  0  0  1   2 |  0  2  1  q
----------------------+----+---------+--------------+---------
  .. o.3x. ..       & |  3 |   3   0 | 40  *  *   * |  1  0  1
  .. .. x.3o.       & |  3 |   3   0 |  * 40  *   * |  1  1  0
((uo .. .. ou))&#zq   |  4 |   0   4 |  *  * 30   * |  0  2  0
  .. ox .. ..  &#q  & |  3 |   1   2 |  *  *  * 120 |  0  1  1
----------------------+----+---------+--------------+---------
  .. o.3x.3o.       & ♦  6 |  12   0 |  4  4  0   0 | 10  *  *
((uo3ox .. ou))&#zq & ♦  9 |   6  12 |  0  2  3   6 |  * 20  *
  .. ox3xo ..  &#q    ♦  6 |   6   6 |  2  0  0   6 |  *  * 20