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 VFfxo2o(-x)ofo3oxoox5ooxoo&#zx. And finally into VFf(-x)o2o(-x)ofo3oxoox5ooxoo&#zx. Then a Stott expansion wrt. the first and second nodes produces this polychoron.

Incidence matrix according to Dynkin symbol

xoxxFxxox3oxoxoxoxo5ooxoooxoo&#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
(ike || pseudo id || pseudo srid || pseudo ti || pseudo F-ike || pseudo ti || pseudo srid || pseudo id || doe)

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