This polychoron is a mere bistratic stack of segmentochora. It not even is a convex one. In fact the dihedral angle at the {3} between the tets of the upper segment is arccos(1/4) = 75.522488° and that at the {3} between tet and trip in the lower segment is arccos(-sqrt(3/8)) = 127.761244°.

Incidence matrix according to Dynkin symbol

oxx3ooo3oox&#xt   → both heights = sqrt(5/8) = 0.790569
(pt || pseudo tet || co)

o..3o..3o..     | 1 *  * ♦ 4 0  0  0  0 | 6 0  0  0 0 0 0 | 4 0 0 0 0
.o.3.o.3.o.     | * 4  * | 1 3  3  0  0 | 3 3  6  3 0 0 0 | 3 3 3 1 0
..o3..o3..o     | * * 12 | 0 0  1  2  2 | 0 0  2  2 1 2 1 | 0 1 2 1 1
----------------+--------+--------------+-----------------+----------
oo.3oo.3oo.&#x  | 1 1  0 | 4 *  *  *  * | 3 0  0  0 0 0 0 | 3 0 0 0 0
.x. ... ...     | 0 2  0 | * 6  *  *  * | 1 2  2  0 0 0 0 | 2 2 1 0 0
.oo3.oo3.oo&#x  | 0 1  1 | * * 12  *  * | 0 0  2  2 0 0 0 | 0 1 2 1 0
..x ... ...     | 0 0  2 | * *  * 12  * | 0 0  1  0 1 1 0 | 0 1 1 0 1
... ... ..x     | 0 0  2 | * *  *  * 12 | 0 0  0  1 0 1 1 | 0 0 1 1 1
----------------+--------+--------------+-----------------+----------
ox. ... ...&#x  | 1 2  0 | 2 1  0  0  0 | 6 *  *  * * * * | 2 0 0 0 0
.x.3.o. ...     | 0 3  0 | 0 3  0  0  0 | * 4  *  * * * * | 1 1 0 0 0
.xx ... ...&#x  | 0 2  2 | 0 1  2  1  0 | * * 12  * * * * | 0 1 1 0 0
... ... .ox&#x  | 0 1  2 | 0 0  2  0  1 | * *  * 12 * * * | 0 0 1 1 0
..x3..o ...     | 0 0  3 | 0 0  0  3  0 | * *  *  * 4 * * | 0 1 0 0 1
..x ... ..x     | 0 0  4 | 0 0  0  2  2 | * *  *  * * 6 * | 0 0 1 0 1
... ..o3..x     | 0 0  3 | 0 0  0  0  3 | * *  *  * * * 4 | 0 0 0 1 1
----------------+--------+--------------+-----------------+----------
ox.3oo. ...&#x  ♦ 1 3  0 | 3 3  0  0  0 | 3 1  0  0 0 0 0 | 4 * * * *
.xx3.oo ...&#x  ♦ 0 3  3 | 0 3  3  3  0 | 0 1  3  0 1 0 0 | * 4 * * *
.xx ... .ox&#x  ♦ 0 2  4 | 0 1  4  2  2 | 0 0  2  2 0 1 0 | * * 6 * *
... .oo3.ox&#x  ♦ 0 1  3 | 0 0  3  0  3 | 0 0  0  3 0 0 1 | * * * 4 *
..x3..o3..x     ♦ 0 0 12 | 0 0  0 12 12 | 0 0  0  0 4 6 4 | * * * * 1