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 third node produces oxofofoxo3oofoxofoo5xxoxxxoxx. This polychoron then will be that diminishing therefrom, which deletes both the first and third layer from either end each.

Incidence matrix according to Dynkin symbol

xfofx3ooxoo5xxxxx&#xt   → height(1,2) = height(4,5) = (1+sqrt(5))/4 = 0.809017
                          height(2,3) = height(3,4) = 1/2
(srid || pseudo (f,x)-srid || pseudo tid || pseudo (f,x)-srid || srid)

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

or
Fxo xfo3oox5xxx&#zxt   → all existing heights = 0

o.. o..3o..5o..     | 120   *  * |   2   2   1  0   0   0  0  0 |  1  2  1   2   2  0  0   0   0   0  0 | 1  1  2  1  0  0  0
.o. .o.3.o.5.o.     |   * 120  * |   0   0   1  1   2   2  0  0 |  0  0  0   2   2  2  1   2   1   2  0 | 0  1  2  1  1  1  2
..o ..o3..o5..o     |   *   * 60 |   0   0   0  0   0   4  2  1 |  0  0  0   2   0  0  0   2   4   4  1 | 0  2  2  0  0  2  2
--------------------+------------+------------------------------+---------------------------------------+--------------------
... x.. ... ...     |   2   0  0 | 120   *   *  *   *   *  *  * |  1  1  0   1   0  0  0   0   0   0  0 | 1  1  1  0  0  0  0
... ... ... x..     |   2   0  0 |   * 120   *  *   *   *  *  * |  0  1  1   0   1  0  0   0   0   0  0 | 1  0  1  1  0  0  0
oo. oo.3oo.5oo.&#x  |   1   1  0 |   *   * 120  *   *   *  *  * |  0  0  0   2   2  0  0   0   0   0  0 | 0  1  2  1  0  0  0
.x. ... ... ...     |   0   2  0 |   *   *   * 60   *   *  *  * |  0  0  0   0   0  2  0   2   0   0  0 | 0  0  0  0  1  1  2
... ... ... .x.     |   0   2  0 |   *   *   *  * 120   *  *  * |  0  0  0   0   1  1  1   0   0   1  0 | 0  0  1  1  1  0  1
.oo .oo3.oo5.oo&#x  |   0   1  1 |   *   *   *  *   * 240  *  * |  0  0  0   1   0  0  0   1   1   1  0 | 0  1  1  0  0  1  1
... ... ..x ...     |   0   0  2 |   *   *   *  *   *   * 60  * |  0  0  0   0   0  0  0   0   2   0  1 | 0  2  0  0  0  1  0
... ... ... ..x     |   0   0  2 |   *   *   *  *   *   *  * 30 |  0  0  0   0   0  0  0   0   0   4  0 | 0  0  2  0  0  0  2
--------------------+------------+------------------------------+---------------------------------------+--------------------
... x..3o.. ...     |   3   0  0 |   3   0   0  0   0   0  0  0 | 40  *  *   *   *  *  *   *   *   *  * | 1  1  0  0  0  0  0
... x.. ... x..     |   4   0  0 |   2   2   0  0   0   0  0  0 |  * 60  *   *   *  *  *   *   *   *  * | 1  0  1  0  0  0  0
... ... o..5x..     |   5   0  0 |   0   5   0  0   0   0  0  0 |  *  * 24   *   *  *  *   *   *   *  * | 1  0  0  1  0  0  0
... xfo ... ...&#xt |   2   2  1 |   1   0   2  0   0   2  0  0 |  *  *  * 120   *  *  *   *   *   *  * | 0  1  1  0  0  0  0
... ... ... xx.&#x  |   2   2  0 |   0   1   2  0   1   0  0  0 |  *  *  *   * 120  *  *   *   *   *  * | 0  0  1  1  0  0  0
.x. ... ... .x.     |   0   4  0 |   0   0   0  2   2   0  0  0 |  *  *  *   *   * 60  *   *   *   *  * | 0  0  0  0  1  0  1
... ... .o.5.x.     |   0   5  0 |   0   0   0  0   5   0  0  0 |  *  *  *   *   *  * 24   *   *   *  * | 0  0  0  1  1  0  0
.xo ... ... ...&#x  |   0   2  1 |   0   0   0  1   0   2  0  0 |  *  *  *   *   *  *  * 120   *   *  * | 0  0  0  0  0  1  1
... ... .ox ...&#x  |   0   1  2 |   0   0   0  0   0   2  1  0 |  *  *  *   *   *  *  *   * 120   *  * | 0  1  0  0  0  1  0
... ... ... .xx&#x  |   0   2  2 |   0   0   0  0   1   2  0  1 |  *  *  *   *   *  *  *   *   * 120  * | 0  0  1  0  0  0  1
... ..o3..x ...     |   0   0  3 |   0   0   0  0   0   0  3  0 |  *  *  *   *   *  *  *   *   *   * 20 | 0  2  0  0  0  0  0
--------------------+------------+------------------------------+---------------------------------------+--------------------
... x..3o..5x..     ♦  60   0  0 |  60  60   0  0   0   0  0  0 | 20 30 12   0   0  0  0   0   0   0  0 | 2  *  *  *  *  *  *
... xfo3oox ...&#xt ♦   3   3  3 |   3   0   3  0   0   6  3  0 |  1  0  0   3   0  0  0   0   3   0  1 | * 40  *  *  *  *  *
... xfo ... xxx&#xt ♦   4   4  2 |   2   2   4  0   2   4  0  1 |  0  1  0   2   2  0  0   0   0   2  0 | *  * 60  *  *  *  *
... ... oo.5xx.&#x  ♦   5   5  0 |   0   5   5  0   5   0  0  0 |  0  0  1   0   5  0  1   0   0   0  0 | *  *  * 24  *  *  *
.x. ... .o.5.x.     ♦   0  10  0 |   0   0   0  5  10   0  0  0 |  0  0  0   0   0  5  2   0   0   0  0 | *  *  *  * 12  *  *
.xo ... .ox ...&#x  ♦   0   2  2 |   0   0   0  1   0   4  1  0 |  0  0  0   0   0  0  0   2   2   0  0 | *  *  *  *  * 60  *
.xo ... ... .xx&#x  ♦   0   4  2 |   0   0   0  2   2   4  0  1 |  0  0  0   0   0  1  0   2   0   2  0 | *  *  *  *  *  * 60