The relation to ex runs as follows: ex in pentic subsymmetry can be given as ((xffoo3oxoof3fooxo3ooffx))&#zx. That will be transformed into ((xFfoo3o(-x)oof3fxoxo3ooffx))&#zx. Then into ((xFfoo3o(-x)oxf3fxo(-x)o3oofFx))&#zx. Finally into ((xFfxo3o(-x)o(-x)f3fxooo3oofFx))&#zx. Then a Stott expansion wrt. the second node produces this polychoron.

The non-existing lacings calculate to vertex distances according to f=(1+sqrt(5))/2.

The structure here is quite striking: The set of 5 tets represents the vertices of a large pen. Pairs of thawroes connect at their hexagonal bases mirror symmetric and attach their top triangles to these tets. Thus those form the edges of that pen. The squippies connect in the obvious way to those thawroes. The remainder of that truss then is filled by more tets, the octs, and the ikes.

Incidence matrix according to Dynkin symbol

((xFfxo3xoxoF3fxooo3oofFx))&#zx   → all heights = 0 – except those of the not existing lacing(1,4), lacing(2,4), lacing(2,5), and lacing(4,5)

o....3o....3o....3o....     | 60  *  *  *  * |  1  1  1   2   2  0   0  0  0  0  0  0 |  1  1  2  2  1   2   2  0  0  0  0  0  0  0  0  0 |  2  1  2 0  0  1  0 0
.o...3.o...3.o...3.o...     |  * 30  *  *  * |  0  0  2   0   0  4   4  0  0  0  0  0 |  0  1  0  0  0   4   0  2  2  2  4  0  0  0  0  0 |  2  0  0 1  2  2  0 0
..o..3..o..3..o..3..o..     |  *  * 60  *  * |  0  0  0   2   0  0   2  2  1  1  0  0 |  0  0  2  0  0   2   2  0  0  2  1  1  2  1  0  0 |  2  0  2 0  1  1  1 0
...o.3...o.3...o.3...o.     |  *  *  * 20  * ♦  0  0  0   0   0  0   0  0  3  0  3  0 |  0  0  0  0  0   0   0  0  0  0  0  0  3  3  3  0 |  0  0  3 0  0  0  1 1
....o3....o3....o3....o     |  *  *  *  * 30 |  0  0  0   0   4  0   0  0  0  2  0  2 |  0  0  0  2  4   0   4  0  0  0  0  0  0  1  0  1 |  0  2  2 0  0  2  0 0
----------------------------+----------------+----------------------------------------+---------------------------------------------------+----------------------
x.... ..... ..... .....     |  2  0  0  0  0 | 30  *  *   *   *  *   *  *  *  *  *  * |  1  0  0  2  0   0   0  0  0  0  0  0  0  0  0  0 |  0  1  2 0  0  0  0 0
..... x.... ..... .....     |  2  0  0  0  0 |  * 30  *   *   *  *   *  *  *  *  *  * |  1  1  2  0  0   0   0  0  0  0  0  0  0  0  0  0 |  2  0  2 0  0  0  0 0
oo...3oo...3oo...3oo...&#x  |  1  1  0  0  0 |  *  * 60   *   *  *   *  *  *  *  *  * |  0  1  0  0  0   2   0  0  0  0  0  0  0  0  0  0 |  2  0  0 0  0  1  0 0
o.o..3o.o..3o.o..3o.o..&#x  |  1  0  1  0  0 |  *  *  * 120   *  *   *  *  *  *  *  * |  0  0  1  0  0   1   1  0  0  0  0  0  0  0  0  0 |  1  0  1 0  0  1  0 0
o...o3o...o3o...o3o...o&#x  |  1  0  0  0  1 |  *  *  *   * 120  *   *  *  *  *  *  * |  0  0  0  1  1   0   1  0  0  0  0  0  0  0  0  0 |  0  1  1 0  0  1  0 0
..... ..... .x... .....     |  0  2  0  0  0 |  *  *  *   *   * 60   *  *  *  *  *  * |  0  0  0  0  0   0   0  1  1  0  1  0  0  0  0  0 |  0  0  0 1  1  1  0 0
.oo..3.oo..3.oo..3.oo..&#x  |  0  1  1  0  0 |  *  *  *   *   *  * 120  *  *  *  *  * |  0  0  0  0  0   1   0  0  0  1  1  0  0  0  0  0 |  1  0  0 0  1  1  0 0
..... ..x.. ..... .....     |  0  0  2  0  0 |  *  *  *   *   *  *   * 60  *  *  *  * |  0  0  1  0  0   0   0  0  0  1  0  1  1  0  0  0 |  1  0  1 0  1  0  1 0
..oo.3..oo.3..oo.3..oo.&#x  |  0  0  1  1  0 |  *  *  *   *   *  *   *  * 60  *  *  * |  0  0  0  0  0   0   0  0  0  0  0  0  2  1  0  0 |  0  0  2 0  0  0  1 0
..o.o3..o.o3..o.o3..o.o&#x  |  0  0  1  0  1 |  *  *  *   *   *  *   *  *  * 60  *  * |  0  0  0  0  0   0   2  0  0  0  0  0  0  1  0  0 |  0  0  2 0  0  1  0 0
...x. ..... ..... .....     |  0  0  0  2  0 |  *  *  *   *   *  *   *  *  *  * 30  * |  0  0  0  0  0   0   0  0  0  0  0  0  0  1  2  0 |  0  0  2 0  0  0  0 1
..... ..... ..... ....x     |  0  0  0  0  2 |  *  *  *   *   *  *   *  *  *  *  * 30 |  0  0  0  0  2   0   0  0  0  0  0  0  0  0  0  1 |  0  1  0 0  0  2  0 0
----------------------------+----------------+----------------------------------------+---------------------------------------------------+----------------------
x....3x.... ..... .....     |  6  0  0  0  0 |  3  3  0   0   0  0   0  0  0  0  0  0 | 10  *  *  *  *   *   *  *  *  *  *  *  *  *  *  * |  0  0  2 0  0  0  0 0
..... xo... ..... .....&#x  |  2  1  0  0  0 |  0  1  2   0   0  0   0  0  0  0  0  0 |  * 30  *  *  *   *   *  *  *  *  *  *  *  *  *  * |  2  0  0 0  0  0  0 0
..... x.x.. ..... .....&#x  |  2  0  2  0  0 |  0  1  0   2   0  0   0  1  0  0  0  0 |  *  * 60  *  *   *   *  *  *  *  *  *  *  *  *  * |  1  0  1 0  0  0  0 0
x...o ..... ..... .....&#x  |  2  0  0  0  1 |  1  0  0   0   2  0   0  0  0  0  0  0 |  *  *  * 60  *   *   *  *  *  *  *  *  *  *  *  * |  0  1  1 0  0  0  0 0
..... ..... ..... o...x&#x  |  1  0  0  0  2 |  0  0  0   0   2  0   0  0  0  0  0  1 |  *  *  *  * 60   *   *  *  *  *  *  *  *  *  *  * |  0  1  0 0  0  1  0 0
ooo..3ooo..3ooo..3ooo..&#x  |  1  1  1  0  0 |  0  0  1   1   0  0   1  0  0  0  0  0 |  *  *  *  *  * 120   *  *  *  *  *  *  *  *  *  * |  1  0  0 0  0  1  0 0
o.o.o3o.o.o3o.o.o3o.o.o&#x  |  1  0  1  0  1 |  0  0  0   1   1  0   0  0  0  1  0  0 |  *  *  *  *  *   * 120  *  *  *  *  *  *  *  *  * |  0  0  1 0  0  1  0 0
..... .o...3.x... .....     |  0  3  0  0  0 |  0  0  0   0   0  3   0  0  0  0  0  0 |  *  *  *  *  *   *   * 20  *  *  *  *  *  *  *  * |  0  0  0 1  1  0  0 0
..... ..... .x...3.o...     |  0  3  0  0  0 |  0  0  0   0   0  3   0  0  0  0  0  0 |  *  *  *  *  *   *   *  * 20  *  *  *  *  *  *  * |  0  0  0 1  0  1  0 0
..... .ox.. ..... .....&#x  |  0  1  2  0  0 |  0  0  0   0   0  0   2  1  0  0  0  0 |  *  *  *  *  *   *   *  *  * 60  *  *  *  *  *  * |  1  0  0 0  1  0  0 0
..... ..... .xo.. .....&#x  |  0  2  1  0  0 |  0  0  0   0   0  1   2  0  0  0  0  0 |  *  *  *  *  *   *   *  *  *  * 60  *  *  *  *  * |  0  0  0 0  1  1  0 0
..... ..x..3..o.. .....     |  0  0  3  0  0 |  0  0  0   0   0  0   0  3  0  0  0  0 |  *  *  *  *  *   *   *  *  *  *  * 20  *  *  *  * |  0  0  0 0  1  0  1 0
..... ..xo. ..... .....&#x  |  0  0  2  1  0 |  0  0  0   0   0  0   0  1  2  0  0  0 |  *  *  *  *  *   *   *  *  *  *  *  * 60  *  *  * |  0  0  1 0  0  0  1 0
..fxo ..... ..... .....&#xt |  0  0  2  2  1 |  0  0  0   0   0  0   0  0  2  2  1  0 |  *  *  *  *  *   *   *  *  *  *  *  *  * 30  *  * |  0  0  2 0  0  0  0 0 (tower: 435)
...x.3...o. ..... .....     |  0  0  0  3  0 |  0  0  0   0   0  0   0  0  0  0  3  0 |  *  *  *  *  *   *   *  *  *  *  *  *  *  * 20  * |  0  0  1 0  0  0  0 1
..... ..... ....o3....x     |  0  0  0  0  3 |  0  0  0   0   0  0   0  0  0  0  0  3 |  *  *  *  *  *   *   *  *  *  *  *  *  *  *  * 10 |  0  0  0 0  0  2  0 0
----------------------------+----------------+----------------------------------------+---------------------------------------------------+----------------------
..... xox.. ..... .....&#x  ♦  2  1  2  0  0 |  0  1  2   2   0  0   2  1  0  0  0  0 |  0  1  1  0  0   2   0  0  0  1  0  0  0  0  0  0 | 60  *  * *  *  *  * *
x...o ..... ..... o...x&#x  ♦  2  0  0  0  2 |  1  0  0   0   4  0   0  0  0  0  0  1 |  0  0  0  2  2   0   0  0  0  0  0  0  0  0  0  0 |  * 30  * *  *  *  * *
x.fxo3x.xoF ..... .....&#xt ♦  6  0  6  3  3 |  3  3  0   6   6  0   0  3  6  6  3  0 |  1  0  3  3  0   0   6  0  0  0  0  0  3  3  1  0 |  *  * 20 *  *  *  * * (tower: 4351)
..... .o...3.x...3.o...     ♦  0  6  0  0  0 |  0  0  0   0   0 12   0  0  0  0  0  0 |  0  0  0  0  0   0   0  4  4  0  0  0  0  0  0  0 |  *  *  * 5  *  *  * *
..... .ox..3.xo.. .....&#x  ♦  0  3  3  0  0 |  0  0  0   0   0  3   6  3  0  0  0  0 |  0  0  0  0  0   0   0  1  0  3  3  1  0  0  0  0 |  *  *  * * 20  *  * *
..... ..... fxo.o3oof.x&#xt ♦  3  3  3  0  3 |  0  0  3   6   6  3   6  0  0  3  0  3 |  0  0  0  0  3   6   6  0  1  0  3  0  0  0  0  1 |  *  *  * *  * 20  * * (tower: 2315)
..... ..xo.3..oo. .....&#x  ♦  0  0  3  1  0 |  0  0  0   0   0  0   0  3  3  0  0  0 |  0  0  0  0  0   0   0  0  0  0  0  1  3  0  0  0 |  *  *  * *  *  * 20 *
...x.3...o.3...o. .....     ♦  0  0  0  4  0 |  0  0  0   0   0  0   0  0  0  0  6  0 |  0  0  0  0  0   0   0  0  0  0  0  0  0  0  4  0 |  *  *  * *  *  *  * 5