The non-regular hexagons {(h,H,H)²} are diagonally elongated squares. Its vertex angles are h = 90° resp. H = 135°.

This polychoron also qualifies as a "partially octa-contracted grico", but then this term would be not unique. In fact there are 2 such, depending on the grico orientation (x3x4x3o versus o3x4x3x wrt. the tessic subset of 8 directions). – The other one would be pibox tico, but belongs to a different expansion sequence.

Incidence matrix according to Dynkin symbol

qo3xx3xw4xo&#zx   → heights = 0
(tegum sum of (q,x,x,x)-gidpith and (x,w)-tah)

o.3o.3o.4o.     | 384  * |   1   1   1   1  0 |  1  1  1  1   1   1  0 | 1  1  1  1
.o3.o3.o4.o     |   * 96 |   0   0   0   4  2 |  0  0  0  2   4   2  1 | 0  2  1  2
----------------+--------+--------------------+------------------------+-----------
.. x. .. ..     |   2  0 | 192   *   *   *  * |  1  1  0  0   1   0  0 | 1  1  0  1
.. .. x. ..     |   2  0 |   * 192   *   *  * |  1  0  1  1   0   0  0 | 1  1  1  0
.. .. .. x.     |   2  0 |   *   * 192   *  * |  0  1  1  0   0   1  0 | 1  0  1  1
oo3oo3oo4oo&#x  |   1  1 |   *   *   * 384  * |  0  0  0  1   1   1  0 | 0  1  1  1
.. .x .. ..     |   0  2 |   *   *   *   * 96 |  0  0  0  0   2   0  1 | 0  2  0  1
----------------+--------+--------------------+------------------------+-----------
.. x.3x. ..     |   6  0 |   3   3   0   0  0 | 64  *  *  *   *   *  * | 1  1  0  0
.. x. .. x.     |   4  0 |   2   0   2   0  0 |  * 96  *  *   *   *  * | 1  0  0  1
.. .. x.4x.     |   8  0 |   0   4   4   0  0 |  *  * 48  *   *   *  * | 1  0  1  0
qo .. xw ..&#zx |   4  2 |   0   2   0   4  0 |  *  *  * 96   *   *  * | 0  1  1  0  {(h,H,H)2}
.. xx .. ..&#x  |   2  2 |   1   0   0   2  1 |  *  *  *  * 192   *  * | 0  1  0  1
.. .. .. xo&#x  |   2  1 |   0   0   1   2  0 |  *  *  *  *   * 192  * | 0  0  1  1
.o3.x .. ..     |   0  3 |   0   0   0   0  3 |  *  *  *  *   *   * 32 | 0  2  0  0
----------------+--------+--------------------+------------------------+-----------
.. x.3x.4x.     ♦  48  0 |  24  24  24   0  0 |  8 12  6  0   0   0  0 | 8  *  *  *
qo3xx3xw ..&#zx ♦  24 12 |  12  12   0  24 12 |  4  0  0  6  12   0  4 | * 16  *  *
qo .. xw4xo&#zx ♦  16  4 |   0   8   8  16  0 |  0  0  2  4   0   8  0 | *  * 24  *
.. xx .. xo&#x  ♦   4  2 |   2   0   2   4  1 |  0  1  0  0   2   2  0 | *  *  * 96