This complex polyhedron can be viewed as the rectified version of either of x₃-3-o₃-4-o₂ or its dual x₂-4-o₃-3-o₃ in the respectively other direction each, re-using the former edge counts for new vertex count, and using the duals of the faces each (somewhere further out) as the two face types in here. These new face types could alternatively be obtained as the respective vertex figures of the pre-images each. As can be read from the symbol, the vertex figure here is the reducible product of the different edge types x₃ . x₂, i.e. embeddable into real polyhedron trip as its 2 base polygons and its 3 lacing edges.

Alternatively it well could be seen as the rhombated form of the Hessian polyhedron. In fact, it happens to be the rectified version of the rectified version thereof.

Incidence matrix according to Dynkin symbol

o3-3-x3-4-o2

.    .    .  | 216 ♦   6 |  2  3
-------------+-----+-----+------
.    x3   .  |   3 | 432 |  1  1
-------------+-----+-----+------
o3-3-x3   .  ♦   8 |   8 | 54  *
.    x3-4-o2 ♦   9 |   6 |  * 72

x3-3-o3-3-x3

.    .    .  | 216 ♦   3   3 |  1  3  1
-------------+-----+---------+---------
x3   .    .  |   3 | 216   * |  1  1  0
.    .    x3 |   3 |   * 216 |  0  1  1
-------------+-----+---------+---------
x3-3-o3   .  ♦   8 |   8   0 | 27  *  *
x3 - 2  - x3 ♦   9 |   3   3 |  * 72  *
.    o3-3-x3 ♦   8 |   0   8 |  *  * 27