This is either the rectification of x₄-3-o₄-4-o₂ or of its dual, i.e. o₄-3-o₄-4-x₂. As such it reuses their common edge counts each for the vertex count in here. The edges and faces can readily be read from the diagram. In fact, the faces are the duals of either of the former faces as well as the corresponding former vertex figures. The vertex figure in here is (a scaled version of) x₄   x₂.

Incidence matrix according to Dynkin symbol

o4-3-x4-4-o2   (N → ∞)

.    .    .  | 12N ♦   8 | 2  4
------------+-----+-----+-----
.    x4   .  |   4 | 24N | 1  1
------------+-----+-----+-----
o4-3-x4   .  ♦  24 |  24 | N  *
.    x4-4-o2 ♦  16 |   8 | * 3N