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

These complex tilings require p to be from 2 (then resulting again in the real squat); 3; 4; 6.

When seen as rectification of x_p-4-o₂-4-o_p, then it uses the former edge count as vertex count, and the faces are the duals of the former faces as well as the former vertex figures.

Incidence matrix according to Dynkin symbol

x2-4-op-4-o2   (N → ∞)

.    .    .  | 2N ♦  p2 | 2p
-------------+----+-----+---
x2   .    .  |  2 | p2N |  2
-------------+----+-----+---
x2-4-op   .  ♦ 2p |  p2 | 2N

op-4-x2-4-op   (N → ∞)

.    .    .  | 2N ♦  p2 | p p
-------------+----+-----+----
.    x2   .  |  2 | p2N | 1 1
-------------+----+-----+----
op-4-x2   .  ♦ 2p |  p2 | N *
.    x2-4-op ♦ 2p |  p2 | * N