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 VFf(-x)o2oxofo3oofox5oo(-x)oo&#zx. Then a Stott expansion wrt. the first and fourth nodes produces this polychoron.

Incidence matrix according to Dynkin symbol

oxoofooxo3oofxoxfoo5xxoxxxoxx&#xt   → height(1,2) = height(8,9) = (sqrt(5)-1)/4 = 0.309017
                                      height(2,3) = height(4,5) = height(5,6) = height(7,8) = 1/2
                                      height(3,4) = height(6,7) = (1+sqrt(5))/4 = 0.809017
(doe || pseudo srid || pseudo f-id || pseudo tid || pseudo (f,x)-srid || pseudo tid || pseudo f-id || pseudo srid || doe)

o........3o........5o........     & | 40   *  *   *  * |  3   3   0   0   0   0   0  0   0  0  0 |  3   3   6  0  0  0   0   0   0  0  0   0   0  0  0   0  0 | 1  1  3  3  0  0  0  0  0  0
.o.......3.o.......5.o.......     & |  * 120  *   *  * |  0   1   2   2   2   0   0  0   0  0  0 |  0   2   2  1  2  1   2   1   2  0  0   0   0  0  0   0  0 | 0  1  2  1  1  2  1  0  0  0
..o......3..o......5..o......     & |  *   * 60   *  * |  0   0   0   0   4   2   0  0   0  0  0 |  0   0   0  0  0  0   2   4   2  1  0   0   0  0  0   0  0 | 0  0  0  0  2  1  2  0  0  0
...o.....3...o.....5...o.....     & |  *   *  * 120  * |  0   0   0   0   0   1   2  1   2  1  0 |  0   0   0  0  0  0   0   2   0  1  1   2   2  2  1   2  0 | 0  0  0  0  1  0  2  1  2  2
....o....3....o....5....o....       |  *   *  *   * 60 |  0   0   0   0   0   0   0  0   4  0  2 |  0   0   0  0  0  0   0   0   0  0  0   2   4  0  0   2  1 | 0  0  0  0  0  0  2  0  1  2
------------------------------------+------------------+-----------------------------------------+------------------------------------------------------------+-----------------------------
......... ......... ........x     & |  2   0  0   0  0 | 60   *   *   *   *   *   *  *   *  *  * |  2   0   2  0  0  0   0   0   0  0  0   0   0  0  0   0  0 | 1  0  1  2  0  0  0  0  0  0
oo.......3oo.......5oo.......&#x  & |  1   1  0   0  0 |  * 120   *   *   *   *   *  *   *  *  * |  0   2   2  0  0  0   0   0   0  0  0   0   0  0  0   0  0 | 0  1  2  1  0  0  0  0  0  0
.x....... ......... .........     & |  0   2  0   0  0 |  *   * 120   *   *   *   *  *   *  *  * |  0   1   0  1  1  0   1   0   0  0  0   0   0  0  0   0  0 | 0  1  1  0  1  1  0  0  0  0
......... ......... .x.......     & |  0   2  0   0  0 |  *   *   * 120   *   *   *  *   *  *  * |  0   0   1  0  1  1   0   0   1  0  0   0   0  0  0   0  0 | 0  0  1  1  0  1  1  0  0  0
.oo......3.oo......5.oo......&#x  & |  0   1  1   0  0 |  *   *   *   * 240   *   *  *   *  *  * |  0   0   0  0  0  0   1   1   1  0  0   0   0  0  0   0  0 | 0  0  0  0  1  1  1  0  0  0
..oo.....3..oo.....5..oo.....&#x  & |  0   0  1   1  0 |  *   *   *   *   * 120   *  *   *  *  * |  0   0   0  0  0  0   0   2   0  1  0   0   0  0  0   0  0 | 0  0  0  0  1  0  2  0  0  0
......... ...x..... .........     & |  0   0  0   2  0 |  *   *   *   *   *   * 120  *   *  *  * |  0   0   0  0  0  0   0   1   0  0  1   1   0  1  0   0  0 | 0  0  0  0  1  0  1  1  1  0
......... ......... ...x.....     & |  0   0  0   2  0 |  *   *   *   *   *   *   * 60   *  *  * |  0   0   0  0  0  0   0   0   0  1  0   0   2  0  1   0  0 | 0  0  0  0  0  0  2  0  0  2
...oo....3...oo....5...oo....&#x  & |  0   0  0   1  1 |  *   *   *   *   *   *   *  * 240  *  * |  0   0   0  0  0  0   0   0   0  0  0   1   1  0  0   1  0 | 0  0  0  0  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  2  1   2  0 | 0  0  0  0  0  0  0  1  2  2
......... ......... ....x....       |  0   0  0   0  2 |  *   *   *   *   *   *   *  *   *  * 60 |  0   0   0  0  0  0   0   0   0  0  0   0   2  0  0   0  1 | 0  0  0  0  0  0  2  0  0  1
------------------------------------+------------------+-----------------------------------------+------------------------------------------------------------+-----------------------------
......... o........5x........     & |  5   0  0   0  0 |  5   0   0   0   0   0   0  0   0  0  0 | 24   *   *  *  *  *   *   *   *  *  *   *   *  *  *   *  * | 1  0  0  1  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  1  1  0  0  0  0  0  0  0
......... ......... xx.......&#x  & |  2   2  0   0  0 |  1   2   0   1   0   0   0  0   0  0  0 |  *   * 120  *  *  *   *   *   *  *  *   *   *  *  *   *  * | 0  0  1  1  0  0  0  0  0  0
.x.......3.o....... .........     & |  0   3  0   0  0 |  0   0   3   0   0   0   0  0   0  0  0 |  *   *   * 40  *  *   *   *   *  *  *   *   *  *  *   *  * | 0  1  0  0  1  0  0  0  0  0
.x....... ......... .x.......     & |  0   4  0   0  0 |  0   0   2   2   0   0   0  0   0  0  0 |  *   *   *  * 60  *   *   *   *  *  *   *   *  *  *   *  * | 0  0  1  0  0  1  0  0  0  0
......... .o.......5.x.......     & |  0   5  0   0  0 |  0   0   0   5   0   0   0  0   0  0  0 |  *   *   *  *  * 24   *   *   *  *  *   *   *  *  *   *  * | 0  0  0  1  0  0  1  0  0  0
.xo...... ......... .........&#x  & |  0   2  1   0  0 |  0   0   1   0   2   0   0  0   0  0  0 |  *   *   *  *  *  * 120   *   *  *  *   *   *  *  *   *  * | 0  0  0  0  1  1  0  0  0  0
......... .ofx..... .........&#x  & |  0   1  2   2  0 |  0   0   0   0   2   2   1  0   0  0  0 |  *   *   *  *  *  *   * 120   *  *  *   *   *  *  *   *  * | 0  0  0  0  1  0  1  0  0  0
......... ......... .xo......&#x  & |  0   2  1   0  0 |  0   0   0   1   2   0   0  0   0  0  0 |  *   *   *  *  *  *   *   * 120  *  *   *   *  *  *   *  * | 0  0  0  0  0  1  1  0  0  0
......... ......... ..ox.....&#x  & |  0   0  1   2  0 |  0   0   0   0   0   2   0  1   0  0  0 |  *   *   *  *  *  *   *   *   * 60  *   *   *  *  *   *  * | 0  0  0  0  0  0  2  0  0  0
...o.....3...x..... .........&#x  & |  0   0  0   3  0 |  0   0   0   0   0   0   3  0   0  0  0 |  *   *   *  *  *  *   *   *   *  * 40   *   *  *  *   *  * | 0  0  0  0  1  0  0  1  0  0
......... ...xo.... .........&#x  & |  0   0  0   2  1 |  0   0   0   0   0   0   1  0   2  0  0 |  *   *   *  *  *  *   *   *   *  *  * 120   *  *  *   *  * | 0  0  0  0  0  0  1  0  1  0
......... ......... ...xx....&#x  & |  0   0  0   2  2 |  0   0   0   0   0   0   0  1   2  0  1 |  *   *   *  *  *  *   *   *   *  *  *   * 120  *  *   *  * | 0  0  0  0  0  0  1  0  0  1
......... ...x.x... .........&#x    |  0   0  0   4  0 |  0   0   0   0   0   0   2  0   0  2  0 |  *   *   *  *  *  *   *   *   *  *  *   *   * 60  *   *  * | 0  0  0  0  0  0  0  1  1  0
......... ......... ...x.x...&#x    |  0   0  0   4  0 |  0   0   0   0   0   0   0  2   0  2  0 |  *   *   *  *  *  *   *   *   *  *  *   *   *  * 30   *  * | 0  0  0  0  0  0  0  0  0  2
...ooo...3...ooo...5...ooo...&#x    |  0   0  0   2  1 |  0   0   0   0   0   0   0  0   2  1  0 |  *   *   *  *  *  *   *   *   *  *  *   *   *  *  * 120  * | 0  0  0  0  0  0  0  0  1  1
......... ....o....5....x....       |  0   0  0   0  5 |  0   0   0   0   0   0   0  0   0  0  5 |  *   *   *  *  *  *   *   *   *  *  *   *   *  *  *   * 12 | 0  0  0  0  0  0  2  0  0  0
------------------------------------+------------------+-----------------------------------------+------------------------------------------------------------+-----------------------------
o........3o........5x........     & ♦ 20   0  0   0  0 | 30   0   0   0   0   0   0  0   0  0  0 | 12   0   0  0  0  0   0   0   0  0  0   0   0  0  0   0  0 | 2  *  *  *  *  *  *  *  *  *
ox.......3oo....... .........&#x  & ♦  1   3  0   0  0 |  0   3   3   0   0   0   0  0   0  0  0 |  0   3   0  1  0  0   0   0   0  0  0   0   0  0  0   0  0 | * 40  *  *  *  *  *  *  *  *
ox....... ......... xx.......&#x  & ♦  2   4  0   0  0 |  1   4   2   2   0   0   0  0   0  0  0 |  0   2   2  0  1  0   0   0   0  0  0   0   0  0  0   0  0 | *  * 60  *  *  *  *  *  *  *
......... oo.......5xx.......&#x  & ♦  5   5  0   0  0 |  5   5   0   5   0   0   0  0   0  0  0 |  1   0   5  0  0  1   0   0   0  0  0   0   0  0  0   0  0 | *  *  * 24  *  *  *  *  *  *
.xoo.....3.ofx..... .........&#xt & ♦  0   3  3   3  0 |  0   0   3   0   6   3   3  0   0  0  0 |  0   0   0  1  0  0   3   3   0  0  1   0   0  0  0   0  0 | *  *  *  * 40  *  *  *  *  *
.xo...... ......... .xo......&#x  & ♦  0   4  1   0  0 |  0   0   2   2   4   0   0  0   0  0  0 |  0   0   0  0  1  0   2   0   2  0  0   0   0  0  0   0  0 | *  *  *  *  * 60  *  *  *  *
......... .ofxo....5.xoxx....&#xt & ♦  0   5  5  10  5 |  0   0   0   5  10  10   5  5  10  0  5 |  0   0   0  0  0  1   0   5   5  5  0   5   5  0  0   0  1 | *  *  *  *  *  * 24  *  *  *
...o.o...3...x.x... .........&#x    ♦  0   0  0   6  0 |  0   0   0   0   0   0   6  0   0  3  0 |  0   0   0  0  0  0   0   0   0  0  2   0   0  3  0   0  0 | *  *  *  *  *  *  * 20  *  *
......... ...xox... .........&#x    ♦  0   0  0   4  1 |  0   0   0   0   0   0   2  0   4  2  0 |  0   0   0  0  0  0   0   0   0  0  0   2   0  1  0   2  0 | *  *  *  *  *  *  *  * 60  *
......... ......... ...xxx...&#x    ♦  0   0  0   4  2 |  0   0   0   0   0   0   0  2   4  2  1 |  0   0   0  0  0  0   0   0   0  0  0   0   2  0  1   2  0 | *  *  *  *  *  *  *  *  * 60