This complex polychoron can be considered to be the mutual Stott expansion either of x_p-4-o₂-3-o₂-3-o₂ by o_p-4-o₂-3-o₂-3-x₂, or the other way round. Accordingly the new vertex count is just the product of the former vertex count with the facet (in here: face) count of its vertex figure. (This clearly will be independent of the chosen starting figure.) Facets here are both the facets of either starting polyhedron (shifted a bit out each) plus the mere prism product of the respective faces by the mutually other edges. The count of the formers clearly gets maintained in this expansion.

In order to derive the other total counts it is best done by considering the new vertex figure. Note, that in here the well-known techniques, derived for real space polytopes, applies directly too, because all the nodes of the to be considered subdiagram have indices 2 only (at least within its measure-free sense), which surely is enough for the here being asked for counts thereof. (The remaining numbers of the incidence matrix then can easily be derived by means of the general incidence matrix relation.)

Incidence matrix according to Dynkin symbol

xp-4-o2-3-o2-3-x2

.    .    .    .  | 4p4 |   3   3  |   3    6   3  |  1  3   3  1 
-----------------+-----+----------+---------------+-------------
xp   .    .    .  |  p  | 12p3  *  |   2    2   0  |  1  2   1  0 
.    .    .    x2 |  2  |   *  6p4 |   0    2   2  |  0  1   2  1 
-----------------+-----+----------+---------------+-------------
xp-4-o2   .    .  ♦  p2 |  2p   0  | 12p2   *   *  |  1  1   0  0 
xp   .    .    x2 ♦ 2p  |   2   p  |   *  12p3  *  |  0  1   1  0 
.    .    o2-3-x2 |  3  |   0   3  |   *    *  4p4 |  0  0   1  1 
-----------------+-----+----------+---------------+-------------
xp-4-o2-3-o2   .  ♦  p3 |  3p2  0  |  3p    0   0  | 4p  *   *  * 
xp-4-o2   .    x2 ♦ 2p2 |  4p   p2 |   2   2p   0  |  * 6p2  *  * 
xp   .    o2-3-x2 ♦ 3p  |   3  3p  |   0    3   p  |  *  *  4p3 * 
.    o2-3-o2-3-x2 ♦  4  |   0   6  |   0    0   4  |  *  *   *  p4