This polychoron most directly is derived as augmentation of prissi with ikepies at all its 24 ikes.

But this then is equivalent to a partial Stott expansion of ex wrt. the same icoic subsymmetry, as prissi itself can be derived from sadi: Ex in icoic subsymmetry can be given as foxo3ooof3xfoo *b3oxfo&#zx. This polychoron then is derived by an expansion wrt. the second node. (Sadi resp. prissi then would just omit the fourth layer each.)

Incidence matrix according to Dynkin symbol

foxo3xxxF3xfoo *b3oxfo&#zx

o...3o...3o... *b3o...     | 96  *  *  * |  2  1   2   2  1  0  0   0  0  0  0  0 |  2  1  2  1  2  2  1   2   2   2  0  0  0  0  0   0  0  0  0 | 1  1  2  2  1  2   2 0  0  0 0
.o..3.o..3.o.. *b3.o..     |  * 96  *  * |  0  0   2   0  0  2  1   2  1  0  0  0 |  0  0  2  2  0  0  0   2   2   0  1  2  1  2  1   2  0  0  0 | 0  2  0  2  2  0   2 1  1  1 0
..o.3..o.3..o. *b3..o.     |  *  * 96  * |  0  0   0   2  0  0  0   2  0  1  2  1 |  0  0  0  0  2  1  0   2   0   2  0  0  2  2  0   2  2  1  1 | 0  0  1  2  0  1   2 0  2  2 1
...o3...o3...o *b3...o     |  *  *  * 24 ♦  0  0   0   0  4  0  0   0  4  0  0  4 |  0  0  0  0  0  0  2   0   8   8  0  0  0  0  2   8  0  0  2 | 0  0  0  0  4  4   8 0  0  4 0
---------------------------+-------------+----------------------------------------+--------------------------------------------------------------+-------------------------------
.... x... ....    ....     |  2  0  0  0 | 96  *   *   *  *  *  *   *  *  *  *  * |  1  1  1  0  1  0  0   0   0   0  0  0  0  0  0   0  0  0  0 | 1  1  1  1  0  0   0 0  0  0 0
.... .... x...    ....     |  2  0  0  0 |  * 48   *   *  *  *  *   *  *  *  *  * |  2  0  0  0  0  2  1   0   0   0  0  0  0  0  0   0  0  0  0 | 1  0  2  0  0  2   0 0  0  0 0
oo..3oo..3oo.. *b3oo..&#x  |  1  1  0  0 |  *  * 192   *  *  *  *   *  *  *  *  * |  0  0  1  1  0  0  0   1   1   0  0  0  0  0  0   0  0  0  0 | 0  1  0  1  1  0   1 0  0  0 0
o.o.3o.o.3o.o. *b3o.o.&#x  |  1  0  1  0 |  *  *   * 192  *  *  *   *  *  *  *  * |  0  0  0  0  1  1  0   1   0   1  0  0  0  0  0   0  0  0  0 | 0  0  1  1  0  1   1 0  0  0 0
o..o3o..o3o..o *b3o..o&#x  |  1  0  0  1 |  *  *   *   * 96  *  *   *  *  *  *  * |  0  0  0  0  0  0  1   0   2   2  0  0  0  0  0   0  0  0  0 | 0  0  0  0  1  2   2 0  0  0 0
.... .x.. ....    ....     |  0  2  0  0 |  *  *   *   *  * 96  *   *  *  *  *  * |  0  0  1  0  0  0  0   0   0   0  1  1  0  1  0   0  0  0  0 | 0  1  0  1  0  0   0 1  1  0 0
.... .... ....    .x..     |  0  2  0  0 |  *  *   *   *  *  * 48   *  *  *  *  * |  0  0  0  2  0  0  0   0   0   0  0  2  0  0  1   0  0  0  0 | 0  2  0  0  2  0   0 1  0  0 0
.oo.3.oo.3.oo. *b3.oo.&#x  |  0  1  1  0 |  *  *   *   *  *  *  * 192  *  *  *  * |  0  0  0  0  0  0  0   1   0   0  0  0  1  1  0   1  0  0  0 | 0  0  0  1  0  0   1 0  1  1 0
.o.o3.o.o3.o.o *b3.o.o&#x  |  0  1  0  1 |  *  *   *   *  *  *  *   * 96  *  *  * |  0  0  0  0  0  0  0   0   2   0  0  0  0  0  1   2  0  0  0 | 0  0  0  0  2  0   2 0  0  1 0
..x. .... ....    ....     |  0  0  2  0 |  *  *   *   *  *  *  *   *  * 48  *  * |  0  0  0  0  0  0  0   0   0   0  0  0  2  0  0   0  2  0  1 | 0  0  0  0  0  0   0 0  2  2 1
.... ..x. ....    ....     |  0  0  2  0 |  *  *   *   *  *  *  *   *  *  * 96  * |  0  0  0  0  1  0  0   0   0   0  0  0  0  1  0   0  1  1  0 | 0  0  1  1  0  0   0 0  1  0 1
..oo3..oo3..oo *b3..oo&#x  |  0  0  1  1 |  *  *   *   *  *  *  *   *  *  *  * 96 |  0  0  0  0  0  0  0   0   0   2  0  0  0  0  0   2  0  0  1 | 0  0  0  0  0  1   2 0  0  2 0
---------------------------+-------------+----------------------------------------+--------------------------------------------------------------+-------------------------------
.... x...3x...    ....     |  6  0  0  0 |  3  3   0   0  0  0  0   0  0  0  0  0 | 32  *  *  *  *  *  *   *   *   *  *  *  *  *  *   *  *  *  * | 1  0  1  0  0  0   0 0  0  0 0
.... x... .... *b3o...     |  3  0  0  0 |  3  0   0   0  0  0  0   0  0  0  0  0 |  * 32  *  *  *  *  *   *   *   *  *  *  *  *  *   *  *  *  * | 1  1  0  0  0  0   0 0  0  0 0
.... xx.. ....    ....&#x  |  2  2  0  0 |  1  0   2   0  0  1  0   0  0  0  0  0 |  *  * 96  *  *  *  *   *   *   *  *  *  *  *  *   *  *  *  * | 0  1  0  1  0  0   0 0  0  0 0
.... .... ....    ox..&#x  |  1  2  0  0 |  0  0   2   0  0  0  1   0  0  0  0  0 |  *  *  * 96  *  *  *   *   *   *  *  *  *  *  *   *  *  *  * | 0  1  0  0  1  0   0 0  0  0 0
.... x.x. ....    ....&#x  |  2  0  2  0 |  1  0   0   2  0  0  0   0  0  0  1  0 |  *  *  *  * 96  *  *   *   *   *  *  *  *  *  *   *  *  *  * | 0  0  1  1  0  0   0 0  0  0 0
.... .... x.o.    ....&#x  |  2  0  1  0 |  0  1   0   2  0  0  0   0  0  0  0  0 |  *  *  *  *  * 96  *   *   *   *  *  *  *  *  *   *  *  *  * | 0  0  1  0  0  1   0 0  0  0 0
.... .... x..o    ....&#x  |  2  0  0  1 |  0  1   0   0  2  0  0   0  0  0  0  0 |  *  *  *  *  *  * 48   *   *   *  *  *  *  *  *   *  *  *  * | 0  0  0  0  0  2   0 0  0  0 0
ooo.3ooo.3ooo. *b3ooo.&#x  |  1  1  1  0 |  0  0   1   1  0  0  0   1  0  0  0  0 |  *  *  *  *  *  *  * 192   *   *  *  *  *  *  *   *  *  *  * | 0  0  0  1  0  0   1 0  0  0 0
oo.o3oo.o3oo.o *b3oo.o&#x  |  1  1  0  1 |  0  0   1   0  1  0  0   0  1  0  0  0 |  *  *  *  *  *  *  *   * 192   *  *  *  *  *  *   *  *  *  * | 0  0  0  0  1  0   1 0  0  0 0
o.oo3o.oo3o.oo *b3o.oo&#x  |  1  0  1  1 |  0  0   0   1  1  0  0   0  0  0  0  1 |  *  *  *  *  *  *  *   *   * 192  *  *  *  *  *   *  *  *  * | 0  0  0  0  0  1   1 0  0  0 0
.o..3.x.. ....    ....     |  0  3  0  0 |  0  0   0   0  0  3  0   0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   * 32  *  *  *  *   *  *  *  * | 0  0  0  0  0  0   0 1  1  0 0
.... .x.. .... *b3.x..     |  0  6  0  0 |  0  0   0   0  0  3  3   0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   *  * 32  *  *  *   *  *  *  * | 0  1  0  0  0  0   0 1  0  0 0
.ox. .... ....    ....&#x  |  0  1  2  0 |  0  0   0   0  0  0  0   2  0  1  0  0 |  *  *  *  *  *  *  *   *   *   *  *  * 96  *  *   *  *  *  * | 0  0  0  0  0  0   0 0  1  1 0
.... .xx. ....    ....&#x  |  0  2  2  0 |  0  0   0   0  0  1  0   2  0  0  1  0 |  *  *  *  *  *  *  *   *   *   *  *  *  * 96  *   *  *  *  * | 0  0  0  1  0  0   0 0  1  0 0
.... .... ....    .x.o&#x  |  0  2  0  1 |  0  0   0   0  0  0  1   0  2  0  0  0 |  *  *  *  *  *  *  *   *   *   *  *  *  *  * 48   *  *  *  * | 0  0  0  0  2  0   0 0  0  0 0
.ooo3.ooo3.ooo *b3.ooo&#x  |  0  1  1  1 |  0  0   0   0  0  0  0   1  1  0  0  1 |  *  *  *  *  *  *  *   *   *   *  *  *  *  *  * 192  *  *  * | 0  0  0  0  0  0   1 0  0  1 0
..x.3..x. ....    ....     |  0  0  6  0 |  0  0   0   0  0  0  0   0  0  3  3  0 |  *  *  *  *  *  *  *   *   *   *  *  *  *  *  *   * 32  *  * | 0  0  0  0  0  0   0 0  1  0 1
.... ..x.3..o.    ....     |  0  0  3  0 |  0  0   0   0  0  0  0   0  0  0  3  0 |  *  *  *  *  *  *  *   *   *   *  *  *  *  *  *   *  * 32  * | 0  0  1  0  0  0   0 0  0  0 1
..xo .... ....    ....&#x  |  0  0  2  1 |  0  0   0   0  0  0  0   0  0  1  0  2 |  *  *  *  *  *  *  *   *   *   *  *  *  *  *  *   *  *  * 48 | 0  0  0  0  0  0   0 0  0  2 0
---------------------------+-------------+----------------------------------------+--------------------------------------------------------------+-------------------------------
.... x...3x... *b3o...     ♦ 12  0  0  0 | 12  6   0   0  0  0  0   0  0  0  0  0 |  4  4  0  0  0  0  0   0   0   0  0  0  0  0  0   0  0  0  0 | 8  *  *  *  *  *   * *  *  * *
.... xx.. .... *b3ox..&#x  ♦  3  6  0  0 |  3  0   6   0  0  3  3   0  0  0  0  0 |  0  1  3  3  0  0  0   0   0   0  0  1  0  0  0   0  0  0  0 | * 32  *  *  *  *   * *  *  * *
.... x.x.3x.o.    ....&#x  ♦  6  0  3  0 |  3  3   0   6  0  0  0   0  0  0  3  0 |  1  0  0  0  3  3  0   0   0   0  0  0  0  0  0   0  0  1  0 | *  * 32  *  *  *   * *  *  * *
.... xxx. ....    ....&#x  ♦  2  2  2  0 |  1  0   2   2  0  1  0   2  0  0  1  0 |  0  0  1  0  1  0  0   2   0   0  0  0  0  1  0   0  0  0  0 | *  *  * 96  *  *   * *  *  * *
.... .... ....    ox.o&#x  ♦  1  2  0  1 |  0  0   2   0  1  0  1   0  2  0  0  0 |  0  0  0  1  0  0  0   0   2   0  0  0  0  0  1   0  0  0  0 | *  *  *  * 96  *   * *  *  * *
.... .... x.oo    ....&#x  ♦  2  0  1  1 |  0  1   0   2  2  0  0   0  0  0  0  1 |  0  0  0  0  0  1  1   0   0   2  0  0  0  0  0   0  0  0  0 | *  *  *  *  * 96   * *  *  * *
oooo3oooo3oooo *b3oooo&#x  ♦  1  1  1  1 |  0  0   1   1  1  0  0   1  1  0  0  1 |  0  0  0  0  0  0  0   1   1   1  0  0  0  0  0   1  0  0  0 | *  *  *  *  *  * 192 *  *  * *
.o..3.x.. .... *b3.x..     ♦  0 12  0  0 |  0  0   0   0  0 12  6   0  0  0  0  0 |  0  0  0  0  0  0  0   0   0   0  4  4  0  0  0   0  0  0  0 | *  *  *  *  *  *   * 8  *  * *
.ox.3.xx. ....    ....&#x  ♦  0  3  6  0 |  0  0   0   0  0  3  0   6  0  3  3  0 |  0  0  0  0  0  0  0   0   0   0  1  0  3  3  0   0  1  0  0 | *  *  *  *  *  *   * * 32  * *
.oxo .... ....    ....&#x  ♦  0  1  2  1 |  0  0   0   0  0  0  0   2  1  1  0  2 |  0  0  0  0  0  0  0   0   0   0  0  0  1  0  0   2  0  0  1 | *  *  *  *  *  *   * *  * 96 *
..x.3..x.3..o.    ....     ♦  0  0 12  0 |  0  0   0   0  0  0  0   0  0  6 12  0 |  0  0  0  0  0  0  0   0   0   0  0  0  0  0  0   0  4  4  0 | *  *  *  *  *  *   * *  *  * 8

or
o...3o...3o... *b3o...    & | 288  * |   2   1   4   1 |  2  1   4   3    1   2   4 |  1  3  2   3   2
...o3...o3...o *b3...o      |   * 24 ♦   0   0   0  12 |  0  0   0   0    6   0  24 |  0  0  0  12   8
----------------------------+--------+-----------------+----------------------------+-----------------
.... x... ....    ....    & |   2  0 | 288   *   *   * |  1  1   2   0    0   0   0 |  1  2  1   0   0
.... .... x...    ....    & |   2  0 |   * 144   *   * |  2  0   0   2    1   0   0 |  1  2  0   2   0
oo..3oo..3oo.. *b3oo..&#x & |   2  0 |   *   * 576   * |  0  0   1   1    0   1   1 |  0  1  1   1   1
o..o3o..o3o..o *b3o..o&#x & |   1  1 |   *   *   * 288 |  0  0   0   0    1   0   4 |  0  0  0   3   2
----------------------------+--------+-----------------+----------------------------+-----------------
.... x...3x...    ....    & |   6  0 |   3   3   0   0 | 96  *   *   *    *   *   * |  1  1  0   0   0
.... x... .... *b3o...    & |   3  0 |   3   0   0   0 |  * 96   *   *    *   *   * |  1  1  0   0   0
.... xx.. ....    ....&#x & |   4  0 |   2   0   2   0 |  *  * 288   *    *   *   * |  0  1  1   0   0
.... .... ....    ox..&#x & |   3  0 |   0   1   2   0 |  *  *   * 288    *   *   * |  0  1  0   1   0
.... .... x..o    ....&#x & |   2  1 |   0   1   0   2 |  *  *   *    * 144   *   * |  0  0  0   2   0
ooo.3ooo.3ooo. *b3ooo.&#x   |   3  0 |   0   0   3   0 |  *  *   *    *   * 192   * |  0  0  1   0   1
oo.o3oo.o3oo.o *b3oo.o&#x & |   2  1 |   0   0   1   2 |  *  *   *    *   *   * 576 |  0  0  0   1   1
----------------------------+--------+-----------------+----------------------------+-----------------
.... x...3x... *b3o...    & ♦  12  0 |  12   6   0   0 |  4  4   0    0   0   0   0 | 24  *  *   *   *
.... xx.. .... *b3ox..&#x & ♦   9  0 |   6   3   6   0 |  1  1   3    3   0   0   0 |  * 96  *   *   *
.... xxx. ....    ....&#x   ♦   6  0 |   3   0   6   0 |  0  0   3    0   0   2   0 |  *  * 96   *   *
.... .... ....    ox.o&#x & ♦   3  1 |   0   1   2   3 |  0  0   0    1   1   0   2 |  *  *  * 288   *
oooo3oooo3oooo *b3oooo&#x   ♦   3  1 |   0   0   3   3 |  0  0   0    0   0   1   3 |  *  *  *   * 192