q-2thah

Looks like a compound of 2 cuhsquahs, and indeed edges, faces, and cells (including the horocell squat) all coincide by pairs. Vertices however are identified, thus providing a Grünbaumian vertex figure in turn.

Incidence matrix

o3o3o4x4/3*a

. . . .      | 2NM |   12 |  12  12 |  4  6  4  verf: q-2thah
-------------+-----+------+---------+---------
. . . x      |   2 | 12NM |   2   2 |  1  2  1
-------------+-----+------+---------+---------
o . . x4/3*a |   4 |    4 | 6NM   * |  1  1  0
. . o4x      |   4 |    4 |   * 6NM |  0  1  1
-------------+-----+------+---------+---------
o3o . x4/3*a |   8 |   12 |   6   0 | NM  *  *  cube
o . o4x4/3*a |  2M |   4M |   M   M |  * 6N  *  squat
. o3o4x      |   8 |   12 |   0   6 |  *  * NM  cube

o3/2o3/2o4x4/3*a

.   .   . .      | 2NM |   12 |  12  12 |  4  6  4  verf: q-2thah
-----------------+-----+------+---------+---------
.   .   . x      |   2 | 12NM |   2   2 |  1  2  1
-----------------+-----+------+---------+---------
o   .   . x4/3*a |   4 |    4 | 6NM   * |  1  1  0
.   .   o4x      |   4 |    4 |   * 6NM |  0  1  1
-----------------+-----+------+---------+---------
o3/2o   . x4/3*a |   8 |   12 |   6   0 | NM  *  *  cube
o   .   o4x4/3*a |  2M |   4M |   M   M |  * 6N  *  squat
.   o3/2o4x      |   8 |   12 |   0   6 |  *  * NM  cube

o3o3/2o4x4*a

. .   . .    | 2NM |   12 |  12  12 |  4  6  4  verf: q-2thah
-------------+-----+------+---------+---------
. .   . x    |   2 | 12NM |   2   2 |  1  2  1
-------------+-----+------+---------+---------
o .   . x4*a |   4 |    4 | 6NM   * |  1  1  0
. .   o4x    |   4 |    4 |   * 6NM |  0  1  1
-------------+-----+------+---------+---------
o3o   . x4*a |   8 |   12 |   6   0 | NM  *  *  cube
o .   o4x4*a |  2M |   4M |   M   M |  * 6N  *  squat
. o3/2o4x    |   8 |   12 |   0   6 |  *  * NM  cube

o3o3/2o4/3x4/3*a

. .   .   .      | 2NM |   12 |  12  12 |  4  6  4  verf: q-2thah
-----------------+-----+------+---------+---------
. .   .   x      |   2 | 12NM |   2   2 |  1  2  1
-----------------+-----+------+---------+---------
o .   .   x4/3*a |   4 |    4 | 6NM   * |  1  1  0
. .   o4/3x      |   4 |    4 |   * 6NM |  0  1  1
-----------------+-----+------+---------+---------
o3o   .   x4/3*a |   8 |   12 |   6   0 | NM  *  *  cube
o .   o4/3x4/3*a |  2M |   4M |   M   M |  * 6N  *  squat
. o3/2o4/3x      |   8 |   12 |   0   6 |  *  * NM  cube