Acronym ... Name Ffxo xofo3ofox5xoxx&#zx Confer uniform relative: ex   related segmentochora: doe || srid   related CRFs: oxofofoxo3oofoxofoo5xxoxxxoxx   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. Then a Stott expansion wrt. the second node produces oxofofoxo3oofoxofoo5xxoxxxoxx. This polychoron then will be the monostratic parabidiminishing therefrom.

Incidence matrix according to Dynkin symbol

```xofofox3ofoxofo5xoxxxox&#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
(srid || pseudo f-id || pseudo (f,x)-srid || pseudo tid || pseudo (f,x)-srid || pseudo f-id || srid)

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

```Ffxo xofo3ofox5xoxx&#zx   → heights = 0

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