The relation to ex runs as follows: ex in pentic subsymmetry can be given as ((xffoo3oxoof3fooxo3ooffx))&#zx. That will be transformed into (((-x)ffoo3xxoof3fooxo3ooffx))&#zx. Then into (((-x)ffoo3xxoxf3foo(-x)o3oofFx))&#zx. Finally a Stott expansion wrt. the first and third node produces this polychoron.

The non-existing lacings calculate to vertex distances according to f=(1+sqrt(5))/2.

Incidence matrix according to Dynkin symbol

((oFFxx3xxoxf3Fxxox3oofFx))&#zx   → all heights = 0 – except those of the not existing lacing(1,2), lacing(1,3), lacing(1,4), and lacing(2,4)

  o....3o....3o....3o....       | 30  *  *  *   * |  2   4  0  0   0   0  0   0   0  0  0   0  0  0  0 |  1  2  2  4  0  0  0  0  0  0   0  0  0  0  0   0  0  0  0  0  0  0  0 |  1  2  2 0  0  0  0  0  0 0  0  0
  .o...3.o...3.o...3.o...       |  * 60  *  *   * |  0   0  1  2   2   2  0   0   0  0  0   0  0  0  0 |  0  0  0  0  2  1  2  2  2  1   2  0  0  0  0   0  0  0  0  0  0  0  0 |  0  1  0 1  2  1  2  0  0 0  0  0
  ..o..3..o..3..o..3..o..       |  *  * 60  *   * |  0   0  0  0   2   0  2   2   2  0  0   0  0  0  0 |  0  0  0  1  0  0  1  2  0  0   2  1  1  2  2   2  0  0  0  0  0  0  0 |  0  1  1 0  1  0  2  1  2 0  0  0
  ...o.3...o.3...o.3...o.       |  *  *  * 60   * |  0   0  0  0   0   0  0   2   0  1  2   2  0  0  0 |  0  0  0  0  0  0  0  0  0  0   0  0  2  1  0   2  2  1  2  1  0  0  0 |  0  0  2 0  0  0  0  1  1 1  1  0
  ....o3....o3....o3....o       |  *  *  *  * 120 |  0   1  0  0   0   1  0   0   1  0  0   1  1  1  1 |  0  1  1  1  0  0  0  0  1  1   1  0  0  0  1   1  0  0  1  1  1  1  1 |  1  1  1 0  0  1  1  0  1 0  1  1
--------------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+----------------------------------
  ..... x.... ..... .....       |  2  0  0  0   0 | 30   *  *  *   *   *  *   *   *  *  *   *  *  *  * |  1  0  0  2  0  0  0  0  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  0
  o...o3o...o3o...o3o...o  &#x  |  1  0  0  0   1 |  * 120  *  *   *   *  *   *   *  *  *   *  *  *  * |  0  1  1  1  0  0  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  0
  ..... .x... ..... .....       |  0  2  0  0   0 |  *   * 30  *   *   *  *   *   *  *  *   *  *  *  * |  0  0  0  0  2  0  2  0  0  0   0  0  0  0  0   0  0  0  0  0  0  0  0 |  0  1  0 1  2  0  0  0  0 0  0  0
  ..... ..... .x... .....       |  0  2  0  0   0 |  *   *  * 60   *   *  *   *   *  *  *   *  *  *  * |  0  0  0  0  1  1  0  1  1  0   0  0  0  0  0   0  0  0  0  0  0  0  0 |  0  0  0 1  1  1  1  0  0 0  0  0
  .oo..3.oo..3.oo..3.oo..  &#x  |  0  1  1  0   0 |  *   *  *  * 120   *  *   *   *  *  *   *  *  *  * |  0  0  0  0  0  0  1  1  0  0   1  0  0  0  0   0  0  0  0  0  0  0  0 |  0  1  0 0  1  0  1  0  0 0  0  0
  .o..o3.o..o3.o..o3.o..o  &#x  |  0  1  0  0   1 |  *   *  *  *   * 120  *   *   *  *  *   *  *  *  * |  0  0  0  0  0  0  0  0  1  1   1  0  0  0  0   0  0  0  0  0  0  0  0 |  0  1  0 0  0  1  1  0  0 0  0  0
  ..... ..... ..x.. .....       |  0  0  2  0   0 |  *   *  *  *   *   * 60   *   *  *  *   *  *  *  * |  0  0  0  0  0  0  0  1  0  0   0  1  0  1  1   0  0  0  0  0  0  0  0 |  0  0  0 0  1  0  1  1  1 0  0  0
  ..oo.3..oo.3..oo.3..oo.  &#x  |  0  0  1  1   0 |  *   *  *  *   *   *  * 120   *  *  *   *  *  *  * |  0  0  0  0  0  0  0  0  0  0   0  0  1  1  0   1  0  0  0  0  0  0  0 |  0  0  1 0  0  0  0  1  1 0  0  0
  ..o.o3..o.o3..o.o3..o.o  &#x  |  0  0  1  0   1 |  *   *  *  *   *   *  *   * 120  *  *   *  *  *  * |  0  0  0  1  0  0  0  0  0  0   1  0  0  0  1   1  0  0  0  0  0  0  0 |  0  1  1 0  0  0  1  0  1 0  0  0
  ...x. ..... ..... .....       |  0  0  0  2   0 |  *   *  *  *   *   *  *   *   * 30  *   *  *  *  * |  0  0  0  0  0  0  0  0  0  0   0  0  0  0  0   0  2  0  2  0  0  0  0 |  0  0  2 0  0  0  0  0  0 1  1  0
  ..... ...x. ..... .....       |  0  0  0  2   0 |  *   *  *  *   *   *  *   *   *  * 60   *  *  *  * |  0  0  0  0  0  0  0  0  0  0   0  0  1  0  0   0  1  1  0  0  0  0  0 |  0  0  1 0  0  0  0  1  0 1  0  0
  ...oo3...oo3...oo3...oo  &#x  |  0  0  0  1   1 |  *   *  *  *   *   *  *   *   *  *  * 120  *  *  * |  0  0  0  0  0  0  0  0  0  0   0  0  0  0  0   1  0  0  1  1  0  0  0 |  0  0  1 0  0  0  0  0  1 0  1  0
  ....x ..... ..... .....       |  0  0  0  0   2 |  *   *  *  *   *   *  *   *   *  *  *   * 60  *  * |  0  1  0  0  0  0  0  0  0  0   0  0  0  0  0   0  0  0  1  0  1  1  0 |  1  0  1 0  0  0  0  0  0 0  1  1
  ..... ..... ....x .....       |  0  0  0  0   2 |  *   *  *  *   *   *  *   *   *  *  *   *  * 60  * |  0  0  0  0  0  0  0  0  1  0   0  0  0  0  1   0  0  0  0  1  1  0  1 |  0  0  0 0  0  1  1  0  1 0  1  1
  ..... ..... ..... ....x       |  0  0  0  0   2 |  *   *  *  *   *   *  *   *   *  *  *   *  *  * 60 |  0  0  1  0  0  0  0  0  0  1   0  0  0  0  0   0  0  0  0  0  0  1  1 |  1  1  0 0  0  1  0  0  0 0  0  1
--------------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+----------------------------------
  o....3x.... ..... .....       |  3  0  0  0   0 |  3   0  0  0   0   0  0   0   0  0  0   0  0  0  0 | 10  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  0  2 0  0  0  0  0  0 0  0  0
  o...x ..... ..... .....  &#x  |  1  0  0  0   2 |  0   2  0  0   0   0  0   0   0  0  0   0  1  0  0 |  * 60  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  1  0  1 0  0  0  0  0  0 0  0  0
  ..... ..... ..... o...x  &#x  |  1  0  0  0   2 |  0   2  0  0   0   0  0   0   0  0  0   0  0  0  1 |  *  * 60  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  1  1  0 0  0  0  0  0  0 0  0  0
  ..... x.o.f ..... .....  &#xt |  2  0  1  0   2 |  1   2  0  0   0   0  0   0   2  0  0   0  0  0  0 |  *  *  * 60  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  1  1 0  0  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  0  0  0 |  *  *  *  * 20  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  0  0 1  1  0  0  0  0 0  0  0
  ..... ..... .x...3.o...       |  0  3  0  0   0 |  0   0  0  3   0   0  0   0   0  0  0   0  0  0  0 |  *  *  *  *  * 20  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  0  0 1  0  1  0  0  0 0  0  0
  ..... .xo.. ..... .....  &#x  |  0  2  1  0   0 |  0   0  1  0   2   0  0   0   0  0  0   0  0  0  0 |  *  *  *  *  *  * 60  *  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  1  0 0  1  0  0  0  0 0  0  0
  ..... ..... .xx.. .....  &#x  |  0  2  2  0   0 |  0   0  0  1   2   0  1   0   0  0  0   0  0  0  0 |  *  *  *  *  *  *  * 60  *  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  0  0 0  1  0  1  0  0 0  0  0
  ..... ..... .x..x .....  &#x  |  0  2  0  0   2 |  0   0  0  1   0   2  0   0   0  0  0   0  0  1  0 |  *  *  *  *  *  *  *  * 60  *   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  0  0 0  0  1  1  0  0 0  0  0
  ..... ..... ..... .o..x  &#x  |  0  1  0  0   2 |  0   0  0  0   0   2  0   0   0  0  0   0  0  0  1 |  *  *  *  *  *  *  *  *  * 60   *  *  *  *  *   *  *  *  *  *  *  *  * |  0  1  0 0  0  1  0  0  0 0  0  0
  .oo.o3.oo.o3.oo.o3.oo.o  &#x  |  0  1  1  0   1 |  0   0  0  0   1   1  0   0   1  0  0   0  0  0  0 |  *  *  *  *  *  *  *  *  *  * 120  *  *  *  *   *  *  *  *  *  *  *  * |  0  1  0 0  0  0  1  0  0 0  0  0
  ..... ..o..3..x.. .....       |  0  0  3  0   0 |  0   0  0  0   0   0  3   0   0  0  0   0  0  0  0 |  *  *  *  *  *  *  *  *  *  *   * 20  *  *  *   *  *  *  *  *  *  *  * |  0  0  0 0  1  0  0  1  0 0  0  0
  ..... ..ox. ..... .....  &#x  |  0  0  1  2   0 |  0   0  0  0   0   0  0   2   0  0  1   0  0  0  0 |  *  *  *  *  *  *  *  *  *  *   *  * 60  *  *   *  *  *  *  *  *  *  * |  0  0  1 0  0  0  0  1  0 0  0  0
  ..... ..... ..xo. .....  &#x  |  0  0  2  1   0 |  0   0  0  0   0   0  1   2   0  0  0   0  0  0  0 |  *  *  *  *  *  *  *  *  *  *   *  *  * 60  *   *  *  *  *  *  *  *  * |  0  0  0 0  0  0  0  1  1 0  0  0
  ..... ..... ..x.x .....  &#x  |  0  0  2  0   2 |  0   0  0  0   0   0  1   0   2  0  0   0  0  1  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  * 60   *  *  *  *  *  *  *  * |  0  0  0 0  0  0  1  0  1 0  0  0
  ..ooo3..ooo3..ooo3..ooo  &#x  |  0  0  1  1   1 |  0   0  0  0   0   0  0   1   1  0  0   1  0  0  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  * 120  *  *  *  *  *  *  * |  0  0  1 0  0  0  0  0  1 0  0  0
  ...x.3...x. ..... .....       |  0  0  0  6   0 |  0   0  0  0   0   0  0   0   0  3  3   0  0  0  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   * 20  *  *  *  *  *  * |  0  0  1 0  0  0  0  0  0 1  0  0
  ..... ...x.3...o. .....       |  0  0  0  3   0 |  0   0  0  0   0   0  0   0   0  0  3   0  0  0  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  * 20  *  *  *  *  * |  0  0  0 0  0  0  0  1  0 1  0  0
  ...xx ..... ..... .....  &#x  |  0  0  0  2   2 |  0   0  0  0   0   0  0   0   0  1  0   2  1  0  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  * 60  *  *  *  * |  0  0  1 0  0  0  0  0  0 0  1  0
  ..... ..... ...ox .....  &#x  |  0  0  0  1   2 |  0   0  0  0   0   0  0   0   0  0  0   2  0  1  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  * 60  *  *  * |  0  0  0 0  0  0  0  0  1 0  1  0
  ....x ..... ....x .....       |  0  0  0  0   4 |  0   0  0  0   0   0  0   0   0  0  0   0  2  2  0 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  * 30  *  * |  0  0  0 0  0  0  0  0  0 0  1  1
  ....x ..... ..... ....x       |  0  0  0  0   4 |  0   0  0  0   0   0  0   0   0  0  0   0  2  0  2 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  * 30  * |  1  0  0 0  0  0  0  0  0 0  0  1
  ..... ..... ....x3....x       |  0  0  0  0   6 |  0   0  0  0   0   0  0   0   0  0  0   0  0  3  3 |  *  *  *  *  *  *  *  *  *  *   *  *  *  *  *   *  *  *  *  *  *  * 20 |  0  0  0 0  0  1  0  0  0 0  0  1
--------------------------------+-----------------+----------------------------------------------------+------------------------------------------------------------------------+----------------------------------
  o...x ..... ..... o...x  &#x  ♦  1  0  0  0   4 |  0   4  0  0   0   0  0   0   0  0  0   0  2  0  2 |  0  2  2  0  0  0  0  0  0  0   0  0  0  0  0   0  0  0  0  0  0  1  0 | 30  *  * *  *  *  *  *  * *  *  *
((..... xxo.f ..... oof.x))&#zx ♦  2  2  2  0   4 |  1   4  1  0   4   4  0   0   4  0  0   0  0  0  2 |  0  0  2  2  0  0  2  0  0  2   4  0  0  0  0   0  0  0  0  0  0  0  0 |  * 30  * *  *  *  *  *  * *  *  * (tower: 1532)
((o.Fxx3x.oxf ..... .....))&#zx ♦  3  0  3  6   6 |  3   6  0  0   0   0  0   6   6  3  3   6  3  0  0 |  1  3  0  3  0  0  0  0  0  0   0  0  3  0  0   6  1  0  3  0  0  0  0 |  *  * 20 *  *  *  *  *  * *  *  * (tower: 1534)
  ..... .x...3.x...3.o...       ♦  0 12  0  0   0 |  0   0  6 12   0   0  0   0   0  0  0   0  0  0  0 |  0  0  0  0  4  4  0  0  0  0   0  0  0  0  0   0  0  0  0  0  0  0  0 |  *  *  * 5  *  *  *  *  * *  *  *
  ..... .xo..3.xx.. .....  &#x  ♦  0  6  3  0   0 |  0   0  3  3   6   0  3   0   0  0  0   0  0  0  0 |  0  0  0  0  1  0  3  3  0  0   0  1  0  0  0   0  0  0  0  0  0  0  0 |  *  *  * * 20  *  *  *  * *  *  *
  ..... ..... .x..x3.o..x  &#x  ♦  0  3  0  0   6 |  0   0  0  3   0   6  0   0   0  0  0   0  0  3  3 |  0  0  0  0  0  1  0  0  3  3   0  0  0  0  0   0  0  0  0  0  0  0  1 |  *  *  * *  * 20  *  *  * *  *  *
  ..... ..... .xx.x .....  &#x  ♦  0  2  2  0   2 |  0   0  0  1   2   2  1   0   2  0  0   0  0  1  0 |  0  0  0  0  0  0  0  1  1  0   2  0  0  0  1   0  0  0  0  0  0  0  0 |  *  *  * *  *  * 60  *  * *  *  *
  ..... ..ox.3..xo. .....  &#x  ♦  0  0  3  3   0 |  0   0  0  0   0   0  3   6   0  0  3   0  0  0  0 |  0  0  0  0  0  0  0  0  0  0   0  1  3  3  0   0  0  1  0  0  0  0  0 |  *  *  * *  *  *  * 20  * *  *  *
  ..... ..... ..xox .....  &#x  ♦  0  0  2  1   2 |  0   0  0  0   0   0  1   2   2  0  0   2  0  1  0 |  0  0  0  0  0  0  0  0  0  0   0  0  0  1  1   2  0  0  0  1  0  0  0 |  *  *  * *  *  *  *  * 60 *  *  *
  ...x.3...x.3...o. .....       ♦  0  0  0 12   0 |  0   0  0  0   0   0  0   0   0  6 12   0  0  0  0 |  0  0  0  0  0  0  0  0  0  0   0  0  0  0  0   0  4  4  0  0  0  0  0 |  *  *  * *  *  *  *  *  * 5  *  *
  ...xx ..... ...ox .....  &#x  ♦  0  0  0  2   4 |  0   0  0  0   0   0  0   0   0  1  0   4  2  2  0 |  0  0  0  0  0  0  0  0  0  0   0  0  0  0  0   0  0  0  2  2  1  0  0 |  *  *  * *  *  *  *  *  * * 30  *
  ....x ..... ....x3....x       ♦  0  0  0  0  12 |  0   0  0  0   0   0  0   0   0  0  0   0  6  6  6 |  0  0  0  0  0  0  0  0  0  0   0  0  0  0  0   0  0  0  0  0  3  3  2 |  *  *  * *  *  *  *  *  * *  * 10