This polychoron is isogonal only. It requires for 2 edge sizes a and d. (c here is a pseudo edge only.)

The transition a → c will result in qoq3ooo3qqo *b3oqq&#zx (rico). Then the a edges also become pseudo ones too, the incidences then would differ accordingly. Esp. the pyritohedral ikes become coes and each adjoin of a regular tet and the 4 adjacent triangular pyramids blends into a cube.

The transition a → 0 will result in ooq3ooo3qoo *b3oqo&#zx (ico). Then the regular tet degenerate into points and the triangular pyramids into edes. And the pyritohedral ikes become octs.

Incidence matrix according to Dynkin symbol

aoc3ooo3cao *b3oca&#zd   → height = 0
                           a < c
                           d = sqrt[(a2-ac+c2)/2]

o..3o..3o.. *b3o..     & | 96 |   3   6 |  3   9  3 |  1  4  3
-------------------------+----+---------+-----------+---------
a.. ... ...    ...     & |  2 | 144   * |  2   2  0 |  1  2  1
oo.3oo.3oo. *b3oo.&#d  & |  2 |   * 288 |  0   2  1 |  0  1  2
-------------------------+----+---------+-----------+---------
a..3o.. ...    ...     & |  3 |   3   0 | 96   *  * |  1  1  0
ao. ... ...    ...&#d  & |  3 |   1   2 |  * 288  * |  0  1  1
ooo3ooo3ooo *b3ooo&#d    |  3 |   0   3 |  *   * 96 |  0  0  2
-------------------------+----+---------+-----------+---------
a..3o.. ... *b3o..     & |  4 |   6   0 |  4   0  0 | 24  *  *  a-tetrahedron
ao.3oo. ...    ...&#d  & |  4 |   3   3 |  1   3  0 |  * 96  *  (a,d)-sized triangular pyramid
aoc ... cao    oca&#zd   | 12 |   6  24 |  0  12  8 |  *  * 24  (a,d)-sized pyritohedral ike