Acronym	...
Name	complex honeycomb xp-4-o2-4-o2, δp,23, complex honeycomb o2-4-xp-4-o2, complex honeycomb xp-4-o2-4-xp
Vertex figure	x2-4-o2
Especially	x2-4-o2-4-o2 (p=2)
Confer	more general: xp-4-o2-4-or       xp-4-o2-4-xr       xp1-q1-or1   xp2-q2-or2   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.

The below also used value q follows the further requirement: 1/p + 2/q + 1/2 = 1, which evaluates into q = 4p/(p-2). Together with the above restriction on p, this leads to the pairs p,q to be one of the followings: 2,∞; 3,12; 4,8; or 6,6.

Incidence matrix according to Dynkin symbol

xp-4-o2-4-o2   (N → ∞)

.    .    .  | p2N ♦   4 |  4
------------+-----+-----+---
xp   .    .  |   p | 4pN |  2
------------+-----+-----+---
xp-4-o2   .  ♦  p2 |  2p | 4N

o2-4-xp-4-o2   (N → ∞)

.    .    .  | p2N ♦   4 |  2  2
------------+-----+-----+------
.    xp   .  |   p | 4pN |  1  1
------------+-----+-----+------
o2-4-xp   .  ♦  p2 |  2p | 2N  *
.    xp-4-o2 ♦  p2 |  2p |  * 2N

xp-4-o2-4-xp   (N → ∞)

.    .    .  | p2N ♦   2   2 | 1  2 1
------------+-----+---------+-------
xp   .    .  |   p | 2pN   * | 1  1 0
.    .    xp |   p |   * 2pN | 0  1 1
------------+-----+---------+-------
xp-4-o2   .  ♦  p2 |  2p   0 | N  * *
xp   .    xp ♦  p2 |   p   p | * 2N *
.    o2-4-xp ♦  p2 |   0  2p | *  * N

xp-q-o2   xp-q-o2   (N → ∞)

.    .    .    .  | p2N ♦   2   2 |  4
-----------------+-----+---------+---
xp   .    .    .  |   p | 2pN   * |  2
.    .    xp   .  |   p |   * 2pN |  2
-----------------+-----+---------+---
xp   .    xp   .  ♦  p2 |   p   p | 4N