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 this polychoron.

Incidence matrix according to Dynkin symbol

xoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt   → height(1,2) = height(3,4) = height(6,7) = height(8,9) = (sqrt(5)-1)/4 = 0.309017
                                      height(2,3) = height(4,5) = height(5,6) = height(7,8) = 1/2
(srid || pseudo tid || pseudo (x,f)-ti || pseudo (F,x)-srid || pseudo grid || pseudo (F,x)-srid || pseudo (x,f)-ti || pseudo tid || srid)

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