Acronym ...
Name complex honeycomb op-4-x2-4-or
Vertex figure xp   xr
Especially op-4-x2-4-op (p=r)   op-4-x2-4-o2 (r=2)   o2-4-x2-4-o2 (p=r=2)  
Confer
general polytopal classes:
complex polytopes  

This is either the rectification of xp-4-o2-4-or or of its dual. As such it reuses that's edge count 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 the former faces as well as the former vertex figures. For vertex figure in here one obviously gets (a scaled version of) xp   xr.


Incidence matrix according to Dynkin symbol

op-4-x2-4-or   (N → ∞)

.    .    .  | 2prN     pr |   r   p
------------+------+-------+--------
.    x2   .  |    2 | p2r2N |   1   1
------------+------+-------+--------
op-4-x2   .     2p |    p2 | r2N   *
.    x2-4-or    2r |    r2 |   * p2N

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