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Note, that the axial-symmetric pseudo-hexagons of the hull also occur in choct. Thence these {(h,H,H)²} would have vertex angles h = arccos(1/3) = 70.528779° resp. H = arccos[-sqrt(2/3)] = 144.735610°. In fact, the hull in here will be just a tetrahedrally-only Stott expanded choct.

Incidence matrix

24  *  *  *  *  * |  1  1  1  1 0  0  0  0  0  0  0 0  0  0 | 1  1  1  1  0 0  0 0  0 0  [4,4,4,6]
 * 12  *  *  *  * |  0  0  2  0 1  1  2  0  0  0  0 0  0  0 | 0  2  0  2  2 0  0 0  0 0  [4,4,4,4,4/3,4/3]
 *  * 12  *  *  * |  0  0  0  0 0  1  0  2  2  0  0 0  0  0 | 0  0  0  0  2 1  2 0  0 0  [3,3,3,4,4]
 *  *  * 12  *  * |  0  0  0  2 0  0  0  0  0  2  1 0  0  0 | 0  0  2  2  0 0  0 1  0 0  [3,4,4,4,4]
 *  *  *  * 12  * |  0  0  0  0 0  0  2  0  0  0  1 1  2  0 | 0  0  0  2  2 0  0 0  2 0  [4,4/3,4/3,4,4/3,4/3]
 *  *  *  *  * 12 |  0  0  0  0 0  0  0  0  2  0  0 0  2  2 | 0  0  0  0  2 0  1 0  2 1  [3,4,4,3,4,4]
------------------+-----------------------------------------+--------------------------
 2  0  0  0  0  0 | 12  *  *  * *  *  *  *  *  *  * *  *  * | 1  1  0  0  0 0  0 0  0 0
 2  0  0  0  0  0 |  * 12  *  * *  *  *  *  *  *  * *  *  * | 1  0  1  0  0 0  0 0  0 0
 1  1  0  0  0  0 |  *  * 24  * *  *  *  *  *  *  * *  *  * | 0  1  0  1  0 0  0 0  0 0
 1  0  0  1  0  0 |  *  *  * 24 *  *  *  *  *  *  * *  *  * | 0  0  1  1  0 0  0 0  0 0
 0  2  0  0  0  0 |  *  *  *  * 6  *  *  *  *  *  * *  *  * | 0  2  0  0  0 0  0 0  0 0
 0  1  1  0  0  0 |  *  *  *  * * 12  *  *  *  *  * *  *  * | 0  0  0  0  2 0  0 0  0 0
 0  1  0  0  1  0 |  *  *  *  * *  * 24  *  *  *  * *  *  * | 0  0  0  1  1 0  0 0  0 0
 0  0  2  0  0  0 |  *  *  *  * *  *  * 12  *  *  * *  *  * | 0  0  0  0  0 1  1 0  0 0
 0  0  1  0  0  1 |  *  *  *  * *  *  *  * 24  *  * *  *  * | 0  0  0  0  1 0  1 0  0 0
 0  0  0  2  0  0 |  *  *  *  * *  *  *  *  * 12  * *  *  * | 0  0  1  0  0 0  0 1  0 0
 0  0  0  1  1  0 |  *  *  *  * *  *  *  *  *  * 12 *  *  * | 0  0  0  2  0 0  0 0  0 0
 0  0  0  0  2  0 |  *  *  *  * *  *  *  *  *  *  * 6  *  * | 0  0  0  0  0 0  0 0  2 0
 0  0  0  0  1  1 |  *  *  *  * *  *  *  *  *  *  * * 24  * | 0  0  0  0  1 0  0 0  1 0
 0  0  0  0  0  2 |  *  *  *  * *  *  *  *  *  *  * *  * 12 | 0  0  0  0  0 0  0 0  1 1
------------------+-----------------------------------------+--------------------------
 6  0  0  0  0  0 |  3  3  0  0 0  0  0  0  0  0  0 0  0  0 | 4  *  *  *  * *  * *  * *  {6}
 2  2  0  0  0  0 |  1  0  2  0 1  0  0  0  0  0  0 0  0  0 | * 12  *  *  * *  * *  * *  {4}
 2  0  0  2  0  0 |  0  1  0  2 0  0  0  0  0  1  0 0  0  0 | *  * 12  *  * *  * *  * *  {4}
 1  1  0  1  1  0 |  0  0  1  1 0  0  1  0  0  0  1 0  0  0 | *  *  * 24  * *  * *  * *  {4}
 0  1  1  0  1  1 |  0  0  0  0 0  1  1  0  1  0  0 0  1  0 | *  *  *  * 24 *  * *  * *  {4}
 0  0  3  0  0  0 |  0  0  0  0 0  0  0  3  0  0  0 0  0  0 | *  *  *  *  * 4  * *  * *  {3}
 0  0  2  0  0  1 |  0  0  0  0 0  0  0  1  2  0  0 0  0  0 | *  *  *  *  * * 12 *  * *  {3}
 0  0  0  3  0  0 |  0  0  0  0 0  0  0  0  0  3  0 0  0  0 | *  *  *  *  * *  * 4  * *  {3}
 0  0  0  0  2  2 |  0  0  0  0 0  0  0  0  0  0  0 1  2  1 | *  *  *  *  * *  * * 12 *  {4}
 0  0  0  0  0  3 |  0  0  0  0 0  0  0  0  0  0  0 0  0  3 | *  *  *  *  * *  * *  * 4  {3}