This complex polychoron can be considered to be the mutual Stott expansion of x₃-3-o₃-3-o₃-3-o₃ with its dual. 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. 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. That one then is x₃-3-o₃ || o₃-3-x₃. (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

x3-3-o3-3-o3-3-x3

.    .    .    .  | 6480 ♦     8     8 |    8    24    8 |   1    8    8   1
-----------------+------+-------------+-----------------+------------------
x3   .    .    .  |    3 | 17280     * |    3     3    0 |   1    3    1   0
.    .    .    x3 |    3 |     * 17280 |    0     3    3 |   0    1    3   1
-----------------+------+-------------+-----------------+------------------
x3-3-o3   .    .  ♦    8 |     8     0 | 6480     *    * |   1    1    0   0
x3   .    .    x3 ♦    9 |     3     3 |    * 17280    * |   0    1    1   0
.    .    o3-3-x3 ♦    8 |     0     8 |    *     * 6480 |   0    0    1   1
-----------------+------+-------------+-----------------+------------------
x3-3-o3-3-o3   .  ♦   27 |    72     0 |   27     0    0 | 240    *    *   *
x3-3-o3   .    x3 ♦   24 |    24     3 |    3     8    0 |   * 2160    *   *
x3   .    o3-3-x3 ♦   24 |     3    24 |    0     8    3 |   *    * 2160   *
.    o3-3-o3-3-x3 ♦   27 |     0    72 |    0     0   27 |   *    *    * 240

or
.    .    .    .     | 6480 ♦    16 |    16    24 |   2   16
--------------------+------+-------+-------------+---------
x3   .    .    .   & |    3 | 34560 |     3     3 |   1    4
--------------------+------+-------+-------------+---------
x3-3-o3   .    .   & ♦    8 |     8 | 12960     * |   1    1
x3   .    .    x3    ♦    9 |     6 |     * 17280 |   0    2
--------------------+------+-------+-------------+---------
x3-3-o3-3-o3   .   & ♦   27 |    72 |    27     0 | 480    *
x3-3-o3   .    x3  & ♦   24 |    27 |     3     8 |   * 4320