Acronym ... Name Ffxo oxFx3xfox5xoxx&#zx Confer uniform relative: ex   related segmentochora: srid || tid   related CRFs: xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt   general polytopal classes: expanded kaleido-facetings

The relation to ex runs as follows: ex in axial icosahedral subsymmetry can be given as VFfxo2oxofo3oooox5ooxoo&#zx = oxofofoxo3ooooxoooo5ooxoooxoo&#xt (F = ff = f+x, V = uf = f+f). That will be transformed into VFfxo2oxofo3oofox5oo(-x)oo&#zx. And finally into VFfxo2o(-x)ofo3oxfox5oo(-x)oo&#zx. Then a Stott expansion wrt. the second and fourth node produces xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt. This polychoron then will be the monostratic parabidiminishing therefrom.

Incidence matrix according to Dynkin symbol

```oxFxFxo3xfoxofx5xoxxxox&#xt   → height(1,2) = height(3,4) = height(4,5) = height(7,8) = 1/2
height(2,3) = height(5,6) = (sqrt(5)-1)/4 = 0.309017
(tid || pseudo (x,f)-ti || pseudo (F,x)-srid || pseudo grid || pseudo (F,x)-srid || pseudo (x,f)-ti || tid)

o......3o......5o......     & | 120   *   *   * |   2  1   2  0   0   0   0   0  0  0  0  0 |  1  2   1   2   2   0   0   0   0  0   0   0  0   0  0  0 | 1  2  1  1  0   0  0  0  0
.o.....3.o.....5.o.....     & |   * 120   *   * |   0  0   2  1   2   2   0   0  0  0  0  0 |  0  0   2   2   1   1   2   1   2  0   0   0  0   0  0  0 | 0  1  2  1  1   1  0  0  0
..o....3..o....5..o....     & |   *   * 120   * |   0  0   0  0   2   0   2   2  1  0  0  0 |  0  0   0   1   0   2   0   0   2  1   1   2  2   2  0  0 | 0  1  1  0  0   2  1  1  2
...o...3...o...5...o...       |   *   *   * 120 |   0  0   0  0   0   2   0   2  0  1  1  1 |  0  0   0   0   0   0   2   2   2  0   2   2  0   1  1  1 | 0  0  2  0  2   2  0  1  1
------------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
....... x...... .......     & |   2   0   0   0 | 120  *   *  *   *   *   *   *  *  *  *  * |  1  1   0   1   0   0   0   0   0  0   0   0  0   0  0  0 | 1  1  1  0  0   0  0  0  0
....... ....... x......     & |   2   0   0   0 |   * 60   *  *   *   *   *   *  *  *  *  * |  0  2   0   0   2   0   0   0   0  0   0   0  0   0  0  0 | 1  2  0  1  0   0  0  0  0
oo.....3oo.....5oo.....&#x  & |   1   1   0   0 |   *  * 240  *   *   *   *   *  *  *  *  * |  0  0   1   1   1   0   0   0   0  0   0   0  0   0  0  0 | 0  1  1  1  0   0  0  0  0
.x..... ....... .......     & |   0   2   0   0 |   *  *   * 60   *   *   *   *  *  *  *  * |  0  0   2   0   0   0   2   0   0  0   0   0  0   0  0  0 | 0  0  2  1  1   0  0  0  0
.oo....3.oo....5.oo....&#x  & |   0   1   1   0 |   *  *   *  * 240   *   *   *  *  *  *  * |  0  0   0   1   0   1   0   0   1  0   0   0  0   0  0  0 | 0  1  1  0  0   1  0  0  0
.o.o...3.o.o...5.o.o...&#x  & |   0   1   0   1 |   *  *   *  *   * 240   *   *  *  *  *  * |  0  0   0   0   0   0   1   1   1  0   0   0  0   0  0  0 | 0  0  1  0  1   1  0  0  0
....... ....... ..x....     & |   0   0   2   0 |   *  *   *  *   *   * 120   *  *  *  *  * |  0  0   0   0   0   1   0   0   0  1   0   1  1   0  0  0 | 0  1  0  0  0   1  1  0  1
..oo...3..oo...5..oo...&#x  & |   0   0   1   1 |   *  *   *  *   *   *   * 240  *  *  *  * |  0  0   0   0   0   0   0   0   1  0   1   1  0   1  0  0 | 0  0  1  0  0   1  0  1  1
..o.o..3..o.o..5..o.o..&#x  & |   0   0   2   0 |   *  *   *  *   *   *   *   * 60  *  *  * |  0  0   0   0   0   0   0   0   0  0   0   0  2   2  0  0 | 0  0  0  0  0   0  1  1  2
...x... ....... .......       |   0   0   0   2 |   *  *   *  *   *   *   *   *  * 60  *  * |  0  0   0   0   0   0   2   0   0  0   2   0  0   0  1  1 | 0  0  2  0  2   0  0  0  0
....... ...x... .......       |   0   0   0   2 |   *  *   *  *   *   *   *   *  *  * 60  * |  0  0   0   0   0   0   0   0   0  0   2   0  0   0  1  0 | 0  0  2  0  0   0  0  1  0
....... ....... ...x...       |   0   0   0   2 |   *  *   *  *   *   *   *   *  *  *  * 60 |  0  0   0   0   0   0   0   2   0  0   0   2  0   0  0  1 | 0  0  0  0  2   2  0  0  1
------------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
o......3x...... .......     & |   3   0   0   0 |   3  0   0  0   0   0   0   0  0  0  0  0 | 40  *   *   *   *   *   *   *   *  *   *   *  *   *  *  * | 1  0  1  0  0   0  0  0  0
....... x......5x......     & |  10   0   0   0 |   5  5   0  0   0   0   0   0  0  0  0  0 |  * 24   *   *   *   *   *   *   *  *   *   *  *   *  *  * | 1  1  0  0  0   0  0  0  0
ox..... ....... .......&#x  & |   1   2   0   0 |   0  0   2  1   0   0   0   0  0  0  0  0 |  *  * 120   *   *   *   *   *   *  *   *   *  *   *  *  * | 0  0  1  1  0   0  0  0  0
....... xfo.... .......&#xt & |   2   2   1   0 |   1  0   2  0   2   0   0   0  0  0  0  0 |  *  *   * 120   *   *   *   *   *  *   *   *  *   *  *  * | 0  1  1  0  0   0  0  0  0
....... ....... xo.....&#x  & |   2   1   0   0 |   0  1   2  0   0   0   0   0  0  0  0  0 |  *  *   *   * 120   *   *   *   *  *   *   *  *   *  *  * | 0  1  0  1  0   0  0  0  0
....... ....... .ox....&#x  & |   0   1   2   0 |   0  0   0  0   2   0   1   0  0  0  0  0 |  *  *   *   *   * 120   *   *   *  *   *   *  *   *  *  * | 0  1  0  0  0   1  0  0  0
.x.x... ....... .......&#x  & |   0   2   0   2 |   0  0   0  1   0   2   0   0  0  1  0  0 |  *  *   *   *   *   * 120   *   *  *   *   *  *   *  *  * | 0  0  1  0  1   0  0  0  0
....... ....... .o.x...&#x  & |   0   1   0   2 |   0  0   0  0   0   2   0   0  0  0  0  1 |  *  *   *   *   *   *   * 120   *  *   *   *  *   *  *  * | 0  0  0  0  1   1  0  0  0
.ooo...3.ooo...5.ooo...&#x  & |   0   1   1   1 |   0  0   0  0   1   1   0   1  0  0  0  0 |  *  *   *   *   *   *   *   * 240  *   *   *  *   *  *  * | 0  0  1  0  0   1  0  0  0
....... ..o....5..x....     & |   0   0   5   0 |   0  0   0  0   0   0   5   0  0  0  0  0 |  *  *   *   *   *   *   *   *   * 24   *   *  *   *  *  * | 0  1  0  0  0   0  1  0  0
....... ..ox... .......&#x  & |   0   0   1   2 |   0  0   0  0   0   0   0   2  0  0  1  0 |  *  *   *   *   *   *   *   *   *  * 120   *  *   *  *  * | 0  0  1  0  0   0  0  1  0
....... ....... ..xx...&#x  & |   0   0   2   2 |   0  0   0  0   0   0   1   2  0  0  0  1 |  *  *   *   *   *   *   *   *   *  *   * 120  *   *  *  * | 0  0  0  0  0   1  0  0  1
....... ....... ..x.x..&#x    |   0   0   4   0 |   0  0   0  0   0   0   2   0  2  0  0  0 |  *  *   *   *   *   *   *   *   *  *   *   * 60   *  *  * | 0  0  0  0  0   0  1  0  1
..ooo..3..ooo..5..ooo..&#x    |   0   0   2   1 |   0  0   0  0   0   0   0   2  1  0  0  0 |  *  *   *   *   *   *   *   *   *  *   *   *  * 120  *  * | 0  0  0  0  0   0  0  1  1
...x...3...x... .......       |   0   0   0   6 |   0  0   0  0   0   0   0   0  0  3  3  0 |  *  *   *   *   *   *   *   *   *  *   *   *  *   * 20  * | 0  0  2  0  0   0  0  0  0
...x... ....... ...x...       |   0   0   0   4 |   0  0   0  0   0   0   0   0  0  2  0  2 |  *  *   *   *   *   *   *   *   *  *   *   *  *   *  * 30 | 0  0  0  0  2   0  0  0  0
------------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
o......3x......5x......     & ♦  60   0   0   0 |  60 30   0  0   0   0   0   0  0  0  0  0 | 20 12   0   0   0   0   0   0   0  0   0   0  0   0  0  0 | 2  *  *  *  *   *  *  *  *
....... xfo....5xox....&#xt & ♦  10   5   5   0 |   5  5  10  0  10   0   5   0  0  0  0  0 |  0  1   0   5   5   5   0   0   0  1   0   0  0   0  0  0 | * 24  *  *  *   *  *  *  *
oxFx...3xfox... .......&#x  & ♦   3   6   3   6 |   3  0   6  3   6   6   0   6  0  3  3  0 |  1  0   3   3   0   0   3   0   6  0   3   0  0   0  1  0 | *  * 40  *  *   *  *  *  *
ox..... ....... xo.....&#x  & ♦   2   2   0   0 |   0  1   4  1   0   0   0   0  0  0  0  0 |  0  0   2   0   2   0   0   0   0  0   0   0  0   0  0  0 | *  *  * 60  *   *  *  *  *
.x.x... ....... .o.x...&#x  & ♦   0   2   0   4 |   0  0   0  1   0   4   0   0  0  2  0  2 |  0  0   0   0   0   0   2   2   0  0   0   0  0   0  0  1 | *  *  *  * 60   *  *  *  *
....... ....... .oxx...&#x  & ♦   0   1   2   2 |   0  0   0  0   2   2   1   2  0  0  0  1 |  0  0   0   0   0   1   0   1   2  0   0   1  0   0  0  0 | *  *  *  *  * 120  *  *  *
....... ..o.o..5..x.x..&#x    ♦   0   0  10   0 |   0  0   0  0   0   0  10   0  5  0  0  0 |  0  0   0   0   0   0   0   0   0  2   0   0  5   0  0  0 | *  *  *  *  *   * 12  *  *
....... ..oxo.. .......&#x    ♦   0   0   2   2 |   0  0   0  0   0   0   0   4  1  0  1  0 |  0  0   0   0   0   0   0   0   0  0   2   0  0   2  0  0 | *  *  *  *  *   *  * 60  *
....... ....... ..xxx..&#x    ♦   0   0   4   2 |   0  0   0  0   0   0   2   4  2  0  0  1 |  0  0   0   0   0   0   0   0   0  0   0   2  1   2  0  0 | *  *  *  *  *   *  *  * 60
```

```Ffxo oxFx3xfox5xoxx&#zx   → heights = 0

o... o...3o...5o...     | 120   *   *   * |   2  1   2  0   0   0  0   0   0  0  0  0 |  1  2   1   2   2   0   0   0   0  0  0   0   0   0  0  0 | 1  2  1  1  0   0  0  0  0
.o.. .o..3.o..5.o..     |   * 120   *   * |   0  0   2  1   2   2  0   0   0  0  0  0 |  0  0   2   2   1   1   2   1   2  0  0   0   0   0  0  0 | 0  1  2  1  1   1  0  0  0
..o. ..o.3..o.5..o.     |   *   * 120   * |   0  0   0  0   2   0  1   2   2  0  0  0 |  0  0   0   1   0   2   0   0   2  2  1   1   2   2  0  0 | 0  1  1  0  0   2  1  1  2
...o ...o3...o5...o     |   *   *   * 120 |   0  0   0  0   0   2  0   0   2  1  1  1 |  0  0   0   0   0   0   2   2   2  0  0   2   2   1  1  1 | 0  0  2  0  2   2  0  1  1
------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
.... .... x... ....     |   2   0   0   0 | 120  *   *  *   *   *  *   *   *  *  *  * |  1  1   0   1   0   0   0   0   0  0  0   0   0   0  0  0 | 1  1  1  0  0   0  0  0  0
.... .... .... x...     |   2   0   0   0 |   * 60   *  *   *   *  *   *   *  *  *  * |  0  2   0   0   2   0   0   0   0  0  0   0   0   0  0  0 | 1  2  0  1  0   0  0  0  0
oo.. oo..3oo..5oo..&#x  |   1   1   0   0 |   *  * 240  *   *   *  *   *   *  *  *  * |  0  0   1   1   1   0   0   0   0  0  0   0   0   0  0  0 | 0  1  1  1  0   0  0  0  0
.... .x.. .... ....     |   0   2   0   0 |   *  *   * 60   *   *  *   *   *  *  *  * |  0  0   2   0   0   0   2   0   0  0  0   0   0   0  0  0 | 0  0  2  1  1   0  0  0  0
.oo. .oo.3.oo.5.oo.&#x  |   0   1   1   0 |   *  *   *  * 240   *  *   *   *  *  *  * |  0  0   0   1   0   1   0   0   1  0  0   0   0   0  0  0 | 0  1  1  0  0   1  0  0  0
.o.o .o.o3.o.o5.o.o&#x  |   0   1   0   1 |   *  *   *  *   * 240  *   *   *  *  *  * |  0  0   0   0   0   0   1   1   1  0  0   0   0   0  0  0 | 0  0  1  0  1   1  0  0  0
..x. .... .... ....     |   0   0   2   0 |   *  *   *  *   *   * 60   *   *  *  *  * |  0  0   0   0   0   0   0   0   0  2  0   0   0   2  0  0 | 0  0  0  0  0   0  1  1  2
.... .... .... ..x.     |   0   0   2   0 |   *  *   *  *   *   *  * 120   *  *  *  * |  0  0   0   0   0   1   0   0   0  1  1   0   1   0  0  0 | 0  1  0  0  0   1  1  0  1
..oo ..oo3..oo5..oo&#x  |   0   0   1   1 |   *  *   *  *   *   *  *   * 240  *  *  * |  0  0   0   0   0   0   0   0   1  0  0   1   1   1  0  0 | 0  0  1  0  0   1  0  1  1
.... ...x .... ....     |   0   0   0   2 |   *  *   *  *   *   *  *   *   * 60  *  * |  0  0   0   0   0   0   2   0   0  0  0   2   0   0  1  1 | 0  0  2  0  2   0  0  0  0
.... .... ...x ....     |   0   0   0   2 |   *  *   *  *   *   *  *   *   *  * 60  * |  0  0   0   0   0   0   0   0   0  0  0   2   0   0  1  0 | 0  0  2  0  0   0  0  1  0
.... .... .... ...x     |   0   0   0   2 |   *  *   *  *   *   *  *   *   *  *  * 60 |  0  0   0   0   0   0   0   2   0  0  0   0   2   0  0  1 | 0  0  0  0  2   2  0  0  1
------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
.... o...3x... ....     |   3   0   0   0 |   3  0   0  0   0   0  0   0   0  0  0  0 | 40  *   *   *   *   *   *   *   *  *  *   *   *   *  *  * | 1  0  1  0  0   0  0  0  0
.... .... x...5x...     |  10   0   0   0 |   5  5   0  0   0   0  0   0   0  0  0  0 |  * 24   *   *   *   *   *   *   *  *  *   *   *   *  *  * | 1  1  0  0  0   0  0  0  0
.... ox.. .... ....&#x  |   1   2   0   0 |   0  0   2  1   0   0  0   0   0  0  0  0 |  *  * 120   *   *   *   *   *   *  *  *   *   *   *  *  * | 0  0  1  1  0   0  0  0  0
.... .... xfo. ....&#xt |   2   2   1   0 |   1  0   2  0   2   0  0   0   0  0  0  0 |  *  *   * 120   *   *   *   *   *  *  *   *   *   *  *  * | 0  1  1  0  0   0  0  0  0
.... .... .... xo..&#x  |   2   1   0   0 |   0  1   2  0   0   0  0   0   0  0  0  0 |  *  *   *   * 120   *   *   *   *  *  *   *   *   *  *  * | 0  1  0  1  0   0  0  0  0
.... .... .... .ox.&#x  |   0   1   2   0 |   0  0   0  0   2   0  0   1   0  0  0  0 |  *  *   *   *   * 120   *   *   *  *  *   *   *   *  *  * | 0  1  0  0  0   1  0  0  0
.... .x.x .... ....&#x  |   0   2   0   2 |   0  0   0  1   0   2  0   0   0  1  0  0 |  *  *   *   *   *   * 120   *   *  *  *   *   *   *  *  * | 0  0  1  0  1   0  0  0  0
.... .... .... .o.x&#x  |   0   1   0   2 |   0  0   0  0   0   2  0   0   0  0  0  1 |  *  *   *   *   *   *   * 120   *  *  *   *   *   *  *  * | 0  0  0  0  1   1  0  0  0
.ooo .ooo3.ooo5.ooo&#x  |   0   1   1   1 |   0  0   0  0   1   1  0   0   1  0  0  0 |  *  *   *   *   *   *   *   * 240  *  *   *   *   *  *  * | 0  0  1  0  0   1  0  0  0
..x. .... .... ..x.     |   0   0   4   0 |   0  0   0  0   0   0  2   2   0  0  0  0 |  *  *   *   *   *   *   *   *   * 60  *   *   *   *  *  * | 0  0  0  0  0   0  1  0  1
.... .... ..o.5..x.     |   0   0   5   0 |   0  0   0  0   0   0  0   5   0  0  0  0 |  *  *   *   *   *   *   *   *   *  * 24   *   *   *  *  * | 0  1  0  0  0   0  1  0  0
.... .... ..ox ....&#x  |   0   0   1   2 |   0  0   0  0   0   0  0   0   2  0  1  0 |  *  *   *   *   *   *   *   *   *  *  * 120   *   *  *  * | 0  0  1  0  0   0  0  1  0
.... .... .... ..xx&#x  |   0   0   2   2 |   0  0   0  0   0   0  0   1   2  0  0  1 |  *  *   *   *   *   *   *   *   *  *  *   * 120   *  *  * | 0  0  0  0  0   1  0  0  1
..xo .... .... ....&#x  |   0   0   2   1 |   0  0   0  0   0   0  1   0   2  0  0  0 |  *  *   *   *   *   *   *   *   *  *  *   *   * 120  *  * | 0  0  0  0  0   0  0  1  1
.... ...x3...x ....     |   0   0   0   6 |   0  0   0  0   0   0  0   0   0  3  3  0 |  *  *   *   *   *   *   *   *   *  *  *   *   *   * 20  * | 0  0  2  0  0   0  0  0  0
.... ...x .... ...x     |   0   0   0   4 |   0  0   0  0   0   0  0   0   0  2  0  2 |  *  *   *   *   *   *   *   *   *  *  *   *   *   *  * 30 | 0  0  0  0  2   0  0  0  0
------------------------+-----------------+-------------------------------------------+-----------------------------------------------------------+---------------------------
.... o...3x...5x...     ♦  60   0   0   0 |  60 30   0  0   0   0  0   0   0  0  0  0 | 20 12   0   0   0   0   0   0   0  0  0   0   0   0  0  0 | 2  *  *  *  *   *  *  *  *
.... .... xfo.5xox.&#xt ♦  10   5   5   0 |   5  5  10  0  10   0  0   5   0  0  0  0 |  0  1   0   5   5   5   0   0   0  0  1   0   0   0  0  0 | * 24  *  *  *   *  *  *  *
.... oxFx3xfox ....&#x  ♦   3   6   3   6 |   3  0   6  3   6   6  0   0   6  3  3  0 |  1  0   3   3   0   0   3   0   6  0  0   3   0   0  1  0 | *  * 40  *  *   *  *  *  *
.... ox.. .... xo..&#x  ♦   2   2   0   0 |   0  1   4  1   0   0  0   0   0  0  0  0 |  0  0   2   0   2   0   0   0   0  0  0   0   0   0  0  0 | *  *  * 60  *   *  *  *  *
.... .x.x .... .o.x&#x  ♦   0   2   0   4 |   0  0   0  1   0   4  0   0   0  2  0  2 |  0  0   0   0   0   0   2   2   0  0  0   0   0   0  0  1 | *  *  *  * 60   *  *  *  *
.... .... .... .oxx&#x  ♦   0   1   2   2 |   0  0   0  0   2   2  0   1   2  0  0  1 |  0  0   0   0   0   1   0   1   2  0  0   0   1   0  0  0 | *  *  *  *  * 120  *  *  *
..x. .... ..o.5..x.     ♦   0   0  10   0 |   0  0   0  0   0   0  5  10   0  0  0  0 |  0  0   0   0   0   0   0   0   0  5  2   0   0   0  0  0 | *  *  *  *  *   * 12  *  *
..xo .... ..ox ....&#x  ♦   0   0   2   2 |   0  0   0  0   0   0  1   0   4  0  1  0 |  0  0   0   0   0   0   0   0   0  0  0   2   0   2  0  0 | *  *  *  *  *   *  * 60  *
..xo .... .... ..xx&#x  ♦   0   0   4   2 |   0  0   0  0   0   0  2   2   4  0  0  1 |  0  0   0   0   0   0   0   0   0  1  0   0   2   2  0  0 | *  *  *  *  *   *  *  * 60
```