This is the rectification of the Witting polychoron. Accordingly it re-uses the edge count of its pre-image as its new vertex count. The new (complex) edge type again will be 3-fold. It will have 2 complex face types, the first being the duals of the ones of its pre-image (which here are Möbius-Kantor polygons again), the others are the faces of the former's vertex figure (likewise Möbius-Kantor polygons). There are 2 complex cell types too, the first being rectified Hessian polyhedra, the others are the former's vertex figures, i.e. (regular) Hessian polyhedra. The new vertex figures in here are the complex reducible polyhedra x₃   x₃-3-o₃.

Incidence matrix according to Dynkin symbol

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

.    .    .    .  | 2160 ♦    24 |    8   24 |   8   3
-----------------+------+-------+-----------+--------
.    x3   .    .  |    3 | 17280 |    1    3 |   3   1
-----------------+------+-------+-----------+--------
o3-3-x3   .    .  ♦    8 |     8 | 2160    * |   3   0
.    x3-3-o3   .  ♦    8 |     8 |    * 6480 |   1   1
-----------------+------+-------+-----------+--------
o3-3-x3-3-o3   .  ♦   72 |   216 |   27   27 | 240   *
.    x3-3-o3-3-o3 ♦   27 |    72 |    0   27 |   * 240