Acronym ... Name xFfxo3xoxoF3fxooo3oofFx&#zx Confer uniform relative: ex   general polytopal classes: expanded kaleido-facetings

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 ..... ..... .....&#zx |  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
...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 ..... .....&#zx ♦  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&#zx ♦  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
```