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 VFfxo2oxofx3oooo(-x)5ooxof&#zx. And finally into VFf(-x)o2oxofx3oooo(-x)5ooxof&#zx. Then a Stott expansion wrt. the first and third nodes produces this polychoron.

It further allows for a bistratically parabidiminishing Fxo oxf3xox5xfo&#zxt too.

Incidence matrix according to Dynkin symbol

oxoxfxoxo3xxxoxoxxx5ooxfofxoo&#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
(id || pseudo ti || pseudo tid || pseudo (x,f)-srid || pseudo (f,x)-ti || pseudo (x,f)-srid || pseudo tid || pseudo ti || id)

o........3o........5o........     & | 60   *   *   *  * |   4   2  0   0   0   0  0   0   0   0  0  0 |  2  2  1   4  0  0   0   0   0  0   0   0   0  0   0  0   0  0 | 1  2  2  0  0  0  0  0  0  0
.o.......3.o.......5.o.......     & |  * 120   *   *  * |   0   1  1   2   2   0  0   0   0   0  0  0 |  0  0  1   2  2  1   2   2   1  0   0   0   0  0   0  0   0  0 | 0  2  1  2  1  1  0  0  0  0
..o......3..o......5..o......     & |  *   * 120   *  * |   0   0  0   0   2   2  1   2   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  1  1  2  1  1  0  0
...o.....3...o.....5...o.....     & |  *   *   * 120  * |   0   0  0   0   0   0  0   2   2   2  1  0 |  0  0  0   0  0  0   0   0   0  0   2   1   2  1   1  2   2  0 | 0  0  0  0  0  1  1  2  1  1
....o....3....o....5....o....       |  *   *   *   * 60 |   0   0  0   0   0   0  0   0   0   4  0  2 |  0  0  0   0  0  0   0   0   0  0   0   0   2  0   4  0   2  1 | 0  0  0  0  0  2  0  1  0  2
------------------------------------+-------------------+---------------------------------------------+----------------------------------------------------------------+-----------------------------
......... 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 | 1  1  1  0  0  0  0  0  0  0
oo.......3oo.......5oo.......&#x  & |  1   1   0   0  0 |   * 120  *   *   *   *  *   *   *   *  *  * |  0  0  1   2  0  0   0   0   0  0   0   0   0  0   0  0   0  0 | 0  2  1  0  0  0  0  0  0  0
.x....... ......... .........     & |  0   2   0   0  0 |   *   * 60   *   *   *  *   *   *   *  *  * |  0  0  1   0  2  0   2   0   0  0   0   0   0  0   0  0   0  0 | 0  2  0  2  1  0  0  0  0  0
......... .x....... .........     & |  0   2   0   0  0 |   *   *  * 120   *   *  *   *   *   *  *  * |  0  0  0   1  1  1   0   1   0  0   0   0   0  0   0  0   0  0 | 0  1  1  1  0  1  0  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  0
......... ..x...... .........     & |  0   0   2   0  0 |   *   *  *   *   * 120  *   *   *   *  *  * |  0  0  0   0  0  0   0   1   0  1   0   1   0  0   0  0   0  0 | 0  0  0  1  0  1  1  0  0  0
......... ......... ..x......     & |  0   0   2   0  0 |   *   *  *   *   *   * 60   *   *   *  *  * |  0  0  0   0  0  0   0   0   2  0   0   0   2  0   0  0   0  0 | 0  0  0  0  1  2  0  1  0  0
..oo.....3..oo.....5..oo.....&#x  & |  0   0   1   1  0 |   *   *  *   *   *   *  * 240   *   *  *  * |  0  0  0   0  0  0   0   0   0  0   1   1   1  0   0  0   0  0 | 0  0  0  0  0  1  1  1  0  0
...x..... ......... .........     & |  0   0   0   2  0 |   *   *  *   *   *   *  *   * 120   *  *  * |  0  0  0   0  0  0   0   0   0  0   1   0   0  1   0  1   0  0 | 0  0  0  0  0  0  1  1  1  0
...oo....3...oo....5...oo....&#x  & |  0   0   0   1  1 |   *   *  *   *   *   *  *   *   * 240  *  * |  0  0  0   0  0  0   0   0   0  0   0   0   1  0   1  0   1  0 | 0  0  0  0  0  1  0  1  0  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  2   2  0 | 0  0  0  0  0  0  0  2  1  1
......... ....x.... .........       |  0   0   0   0  2 |   *   *  *   *   *   *  *   *   *   *  * 60 |  0  0  0   0  0  0   0   0   0  0   0   0   0  0   2  0   0  1 | 0  0  0  0  0  2  0  0  0  1
------------------------------------+-------------------+---------------------------------------------+----------------------------------------------------------------+-----------------------------
o........3x........ .........     & |  3   0   0   0  0 |   3   0  0   0   0   0  0   0   0   0  0  0 | 40  *  *   *  *  *   *   *   *  *   *   *   *  *   *  *   *  * | 1  1  0  0  0  0  0  0  0  0
......... x........5o........     & |  5   0   0   0  0 |   5   0  0   0   0   0  0   0   0   0  0  0 |  * 24  *   *  *  *   *   *   *  *   *   *   *  *   *  *   *  * | 1  0  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  0 |  *  * 60   *  *  *   *   *   *  *   *   *   *  *   *  *   *  * | 0  2  0  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  0 |  *  *  * 120  *  *   *   *   *  *   *   *   *  *   *  *   *  * | 0  1  1  0  0  0  0  0  0  0
.x.......3.x....... .........     & |  0   6   0   0  0 |   0   0  3   3   0   0  0   0   0   0  0  0 |  *  *  *   * 40  *   *   *   *  *   *   *   *  *   *  *   *  * | 0  1  0  1  0  0  0  0  0  0
......... .x.......5.o.......     & |  0   5   0   0  0 |   0   0  0   5   0   0  0   0   0   0  0  0 |  *  *  *   *  * 24   *   *   *  *   *   *   *  *   *  *   *  * | 0  0  1  0  0  1  0  0  0  0
.xo...... ......... .........&#x  & |  0   2   1   0  0 |   0   0  1   0   2   0  0   0   0   0  0  0 |  *  *  *   *  *  * 120   *   *  *   *   *   *  *   *  *   *  * | 0  0  0  1  1  0  0  0  0  0
......... .xx...... .........&#x  & |  0   2   2   0  0 |   0   0  0   1   2   1  0   0   0   0  0  0 |  *  *  *   *  *  *   * 120   *  *   *   *   *  *   *  *   *  * | 0  0  0  1  0  1  0  0  0  0
......... ......... .ox......&#x  & |  0   1   2   0  0 |   0   0  0   0   2   0  1   0   0   0  0  0 |  *  *  *   *  *  *   *   * 120  *   *   *   *  *   *  *   *  * | 0  0  0  0  1  1  0  0  0  0
..o......3..x...... .........     & |  0   0   3   0  0 |   0   0  0   0   0   3  0   0   0   0  0  0 |  *  *  *   *  *  *   *   *   * 40   *   *   *  *   *  *   *  * | 0  0  0  1  0  0  1  0  0  0
..ox..... ......... .........&#x  & |  0   0   1   2  0 |   0   0  0   0   0   0  0   2   1   0  0  0 |  *  *  *   *  *  *   *   *   *  * 120   *   *  *   *  *   *  * | 0  0  0  0  0  0  1  1  0  0
......... ..xo..... .........&#x  & |  0   0   2   1  0 |   0   0  0   0   0   1  0   2   0   0  0  0 |  *  *  *   *  *  *   *   *   *  *   * 120   *  *   *  *   *  * | 0  0  0  0  0  1  1  0  0  0
......... ......... ..xfo....&#xt & |  0   0   2   2  1 |   0   0  0   0   0   0  1   2   0   2  0  0 |  *  *  *   *  *  *   *   *   *  *   *   * 120  *   *  *   *  * | 0  0  0  0  0  1  0  1  0  0
...x.....3...o..... .........     & |  0   0   0   3  0 |   0   0  0   0   0   0  0   0   3   0  0  0 |  *  *  *   *  *  *   *   *   *  *   *   *   * 40   *  *   *  * | 0  0  0  0  0  0  1  0  1  0
......... ...ox.... .........&#x  & |  0   0   0   1  2 |   0   0  0   0   0   0  0   0   0   2  0  1 |  *  *  *   *  *  *   *   *   *  *   *   *   *  * 120  *   *  * | 0  0  0  0  0  1  0  0  0  1
...x.x... ......... .........&#x    |  0   0   0   4  0 |   0   0  0   0   0   0  0   0   2   0  2  0 |  *  *  *   *  *  *   *   *   *  *   *   *   *  *   * 60   *  * | 0  0  0  0  0  0  0  1  1  0
...ooo...3...ooo...5...ooo...&#x    |  0   0   0   2  1 |   0   0  0   0   0   0  0   0   0   2  1  0 |  *  *  *   *  *  *   *   *   *  *   *   *   *  *   *  * 120  * | 0  0  0  0  0  0  0  1  0  1
......... ....x....5....o....       |  0   0   0   0  5 |   0   0  0   0   0   0  0   0   0   0  0  5 |  *  *  *   *  *  *   *   *   *  *   *   *   *  *   *  *   * 12 | 0  0  0  0  0  2  0  0  0  0
------------------------------------+-------------------+---------------------------------------------+----------------------------------------------------------------+-----------------------------
o........3x........5o........     & ♦ 30   0   0   0  0 |  60   0  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   0  0 | 2  *  *  *  *  *  *  *  *  *
ox.......3xx....... .........&#x  & ♦  3   6   0   0  0 |   3   6  3   3   0   0  0   0   0   0  0  0 |  1  0  3   3  1  0   0   0   0  0   0   0   0  0   0  0   0  0 | * 40  *  *  *  *  *  *  *  *
......... xx.......5oo.......&#x  & ♦  5   5   0   0  0 |   5   5  0   5   0   0  0   0   0   0  0  0 |  0  1  0   5  0  1   0   0   0  0   0   0   0  0   0  0   0  0 | *  * 24  *  *  *  *  *  *  *
.xo......3.xx...... .........&#x  & ♦  0   6   3   0  0 |   0   0  3   3   6   3  0   0   0   0  0  0 |  0  0  0   0  1  0   3   3   0  1   0   0   0  0   0  0   0  0 | *  *  * 40  *  *  *  *  *  *
.xo...... ......... .ox......&#x  & ♦  0   2   2   0  0 |   0   0  1   0   4   0  1   0   0   0  0  0 |  0  0  0   0  0  0   2   0   2  0   0   0   0  0   0  0   0  0 | *  *  *  * 60  *  *  *  *  *
......... .xxox....5.oxfo....&#xt & ♦  0   5  10   5  5 |   0   0  0   5  10   5  5  10   0  10  0  5 |  0  0  0   0  0  1   0   5   5  0   0   5   5  0   5  0   0  1 | *  *  *  *  * 24  *  *  *  *
..ox.....3..xo..... .........&#x  & ♦  0   0   3   3  0 |   0   0  0   0   0   3  0   6   3   0  0  0 |  0  0  0   0  0  0   0   0   0  1   3   3   0  1   0  0   0  0 | *  *  *  *  *  * 40  *  *  *
..oxfxo.. ......... ..xfofx..&#xt   ♦  0   0   4   8  2 |   0   0  0   0   0   0  2   8   4   8  4  0 |  0  0  0   0  0  0   0   0   0  0   4   0   4  0   0  2   4  0 | *  *  *  *  *  *  * 30  *  *
...x.x...3...o.o... .........&#x    ♦  0   0   0   6  0 |   0   0  0   0   0   0  0   0   6   0  3  0 |  0  0  0   0  0  0   0   0   0  0   0   0   0  2   0  3   0  0 | *  *  *  *  *  *  *  * 20  *
......... ...oxo... .........&#x    ♦  0   0   0   2  2 |   0   0  0   0   0   0  0   0   0   4  1  1 |  0  0  0   0  0  0   0   0   0  0   0   0   0  0   2  0   2  0 | *  *  *  *  *  *  *  *  * 60