Acronym ... Name oFxFox5AxFoFx2oxofox5ooxofx&#zx Lace cityin approx. ASCII-art ``` x5x x5x F5o o5F o5F x5x x5x F5x x5F x5F F5o F5o F5x F5x x5x o5A x5x x5F x5F o5F o5F F5x F5x x5F x5x x5x F5o F5o o5F x5x x5x ``` Confer uniform relative: ex   general polytopal classes: expanded kaleido-facetings

The relation to ex runs as follows: ex in pentagonal duoprismatic subsymmetry can be given as xfooxo5xofxoo oxofox5ooxofx&#zx (F = ff = f+x, V = uf = f+f). That will be transformed into (-x)fooxo5Fofxoo oxofox5ooxofx&#zx. Then into (-x)fofxo5Fof(-x)oo oxofox5ooxofx&#zx. And finally into (-x)fof(-x)o5Fof(-x)fo oxofox5ooxofx&#zx. Then a Stott expansion wrt. the first and second nodes produces this polychoron.

Incidence matrix according to Dynkin symbol

```oFxFox5AxFoFx oxofox5ooxofx&#zx   → all heights = 0 – except those of the not existing lacing(1,2), lacing(1,4), lacing(1,5), lacing(1,6), lacing(2,5), lacing(2,6), lacing(3,4), lacing(3,6), and lacing(4,5)

o.....5o..... o.....5o.....     | 5  *  *  *  *   * ♦ 10  0  0   0  0  1  0  0   0   0  0  0  0  0 |  5 10  0  0  0  0  0   0  0  0  0  0  0  0  0  0  0  0  0 |  5  2 0  0  0  0  0 0 0
.o....5.o.... .o....5.o....     | * 50  *  *  *   * |  0  1  2   2  1  0  0  0   0   0  0  0  0  0 |  0  0  2  1  2  1  1   2  0  0  0  0  0  0  0  0  0  0  0 |  0  1 1  1  2  0  0 0 0
..o...5..o... ..o...5..o...     | *  * 50  *  *   * |  1  0  0   2  0  1  2  1   0   0  0  0  0  0 |  1  2  0  0  1  2  0   2  2  1  0  0  0  0  0  0  0  0  0 |  2  1 0  2  1  0  0 0 0
...o..5...o.. ...o..5...o..     | *  *  * 25  *   * |  0  0  0   0  2  0  0  0   4   0  0  0  0  0 |  0  0  0  0  0  0  1   4  0  0  2  2  0  0  0  0  0  0  0 |  0  0 0  2  2  1  0 0 0
....o.5....o. ....o.5....o.     | *  *  *  * 25   * |  0  0  0   0  0  0  0  2   0   4  0  0  0  0 |  0  0  0  0  0  0  0   4  0  1  0  0  2  2  0  0  0  0  0 |  0  0 0  2  2  0  1 0 0
.....o5.....o .....o5.....o     | *  *  *  *  * 100 |  0  0  0   0  0  0  0  0   1   1  1  1  1  1 |  0  0  0  0  0  0  0   1  0  0  1  1  1  1  1  1  1  1  1 |  0  0 0  1  1  1  1 1 1
--------------------------------+-------------------+----------------------------------------------+-----------------------------------------------------------+------------------------
o.o...5o.o... o.o...5o.o...&#x  | 1  0  1  0  0   0 | 50  *  *   *  *  *  *  *   *   *  *  *  *  * |  1  2  0  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   0 |  * 25  *   *  *  *  *  *   *   *  *  *  *  * |  0  0  2  0  0  0  1   0  0  0  0  0  0  0  0  0  0  0  0 |  0  0 1  0  2  0  0 0 0
...... ...... .x.... ......     | 0  2  0  0  0   0 |  *  * 50   *  *  *  *  *   *   *  *  *  *  * |  0  0  1  1  1  0  0   0  0  0  0  0  0  0  0  0  0  0  0 |  0  1 1  0  1  0  0 0 0
.oo...5.oo... .oo...5.oo...&#x  | 0  1  1  0  0   0 |  *  *  * 100  *  *  *  *   *   *  *  *  *  * |  0  0  0  0  1  1  0   1  0  0  0  0  0  0  0  0  0  0  0 |  0  1 0  1  1  0  0 0 0
.o.o..5.o.o.. .o.o..5.o.o..&#x  | 0  1  0  1  0   0 |  *  *  *   * 50  *  *  *   *   *  *  *  *  * |  0  0  0  0  0  0  1   2  0  0  0  0  0  0  0  0  0  0  0 |  0  0 0  1  2  0  0 0 0
..x... ...... ...... ......     | 0  0  2  0  0   0 |  *  *  *   *  * 25  *  *   *   *  *  *  *  * |  1  0  0  0  0  0  0   0  2  1  0  0  0  0  0  0  0  0  0 |  2  0 0  2  0  0  0 0 0
...... ...... ...... ..x...     | 0  0  2  0  0   0 |  *  *  *   *  *  * 50  *   *   *  *  *  *  * |  0  1  0  0  0  1  0   0  1  0  0  0  0  0  0  0  0  0  0 |  1  1 0  1  0  0  0 0 0
..o.o.5..o.o. ..o.o.5..o.o.&#x  | 0  0  1  0  1   0 |  *  *  *   *  *  *  * 50   *   *  *  *  *  * |  0  0  0  0  0  0  0   2  0  1  0  0  0  0  0  0  0  0  0 |  0  0 0  2  1  0  0 0 0
...o.o5...o.o ...o.o5...o.o&#x  | 0  0  0  1  0   1 |  *  *  *   *  *  *  *  * 100   *  *  *  *  * |  0  0  0  0  0  0  0   1  0  0  1  1  0  0  0  0  0  0  0 |  0  0 0  1  1  1  0 0 0
....oo5....oo ....oo5....oo&#x  | 0  0  0  0  1   1 |  *  *  *   *  *  *  *  *   * 100  *  *  *  * |  0  0  0  0  0  0  0   1  0  0  0  0  1  1  0  0  0  0  0 |  0  0 0  1  1  0  1 0 0
.....x ...... ...... ......     | 0  0  0  0  0   2 |  *  *  *   *  *  *  *  *   *   * 50  *  *  * |  0  0  0  0  0  0  0   0  0  0  0  0  1  0  1  1  1  0  0 |  0  0 0  1  0  0  1 1 1
...... .....x ...... ......     | 0  0  0  0  0   2 |  *  *  *   *  *  *  *  *   *   *  * 50  *  * |  0  0  0  0  0  0  0   0  0  0  1  0  0  0  1  0  0  1  1 |  0  0 0  0  1  1  0 1 1
...... ...... .....x ......     | 0  0  0  0  0   2 |  *  *  *   *  *  *  *  *   *   *  *  * 50  * |  0  0  0  0  0  0  0   0  0  0  0  0  0  1  0  1  0  1  0 |  0  0 0  0  1  0  1 1 0
...... ...... ...... .....x     | 0  0  0  0  0   2 |  *  *  *   *  *  *  *  *   *   *  *  *  * 50 |  0  0  0  0  0  0  0   0  0  0  0  1  0  0  0  0  1  0  1 |  0  0 0  1  0  1  0 0 1
--------------------------------+-------------------+----------------------------------------------+-----------------------------------------------------------+------------------------
o.x... ...... ...... ......&#x  | 1  0  2  0  0   0 |  2  0  0   0  0  1  0  0   0   0  0  0  0  0 | 25  *  *  *  *  *  *   *  *  *  *  *  *  *  *  *  *  *  * |  2  0 0  0  0  0  0 0 0
...... ...... ...... o.x...&#x  | 1  0  2  0  0   0 |  2  0  0   0  0  0  1  0   0   0  0  0  0  0 |  * 50  *  *  *  *  *   *  *  *  *  *  *  *  *  *  *  *  * |  1  1 0  0  0  0  0 0 0
...... .x.... .x.... ......     | 0  4  0  0  0   0 |  0  2  2   0  0  0  0  0   0   0  0  0  0  0 |  *  * 25  *  *  *  *   *  *  *  *  *  *  *  *  *  *  *  * |  0  0 1  0  1  0  0 0 0
...... ...... .x....5.o....     | 0  5  0  0  0   0 |  0  0  5   0  0  0  0  0   0   0  0  0  0  0 |  *  *  * 10  *  *  *   *  *  *  *  *  *  *  *  *  *  *  * |  0  1 1  0  0  0  0 0 0
...... ...... .xo... ......&#x  | 0  2  1  0  0   0 |  0  0  1   2  0  0  0  0   0   0  0  0  0  0 |  *  *  *  * 50  *  *   *  *  *  *  *  *  *  *  *  *  *  * |  0  1 0  0  1  0  0 0 0
...... ...... ...... .ox...&#x  | 0  1  2  0  0   0 |  0  0  0   2  0  0  1  0   0   0  0  0  0  0 |  *  *  *  *  * 50  *   *  *  *  *  *  *  *  *  *  *  *  * |  0  1 0  1  0  0  0 0 0
...... .x.o.. ...... ......&#x  | 0  2  0  1  0   0 |  0  1  0   0  2  0  0  0   0   0  0  0  0  0 |  *  *  *  *  *  * 25   *  *  *  *  *  *  *  *  *  *  *  * |  0  0 0  0  2  0  0 0 0
.ooooo5.ooooo .ooooo5.ooooo&#xr | 0  1  1  1  1   1 |  0  0  0   1  1  0  0  1   1   1  0  0  0  0 |  *  *  *  *  *  *  * 100  *  *  *  *  *  *  *  *  *  *  * |  0  0 0  1  1  0  0 0 0
..x... ...... ...... ..x...     | 0  0  4  0  0   0 |  0  0  0   0  0  2  2  0   0   0  0  0  0  0 |  *  *  *  *  *  *  *   * 25  *  *  *  *  *  *  *  *  *  * |  1  0 0  1  0  0  0 0 0
..x.o. ...... ...... ......&#x  | 0  0  2  0  1   0 |  0  0  0   0  0  1  0  2   0   0  0  0  0  0 |  *  *  *  *  *  *  *   *  * 25  *  *  *  *  *  *  *  *  * |  0  0 0  2  0  0  0 0 0
...... ...o.x ...... ......&#x  | 0  0  0  1  0   2 |  0  0  0   0  0  0  0  0   2   0  0  1  0  0 |  *  *  *  *  *  *  *   *  *  * 50  *  *  *  *  *  *  *  * |  0  0 0  0  1  1  0 0 0
...... ...... ...... ...o.x&#x  | 0  0  0  1  0   2 |  0  0  0   0  0  0  0  0   2   0  0  0  0  1 |  *  *  *  *  *  *  *   *  *  *  * 50  *  *  *  *  *  *  * |  0  0 0  1  0  1  0 0 0
....ox ...... ...... ......&#x  | 0  0  0  0  1   2 |  0  0  0   0  0  0  0  0   0   2  1  0  0  0 |  *  *  *  *  *  *  *   *  *  *  *  * 50  *  *  *  *  *  * |  0  0 0  1  0  0  1 0 0
...... ...... ....ox ......&#x  | 0  0  0  0  1   2 |  0  0  0   0  0  0  0  0   0   2  0  0  1  0 |  *  *  *  *  *  *  *   *  *  *  *  *  * 50  *  *  *  *  * |  0  0 0  0  1  0  1 0 0
.....x5.....x ...... ......     | 0  0  0  0  0  10 |  0  0  0   0  0  0  0  0   0   0  5  5  0  0 |  *  *  *  *  *  *  *   *  *  *  *  *  *  * 10  *  *  *  * |  0  0 0  0  0  0  0 1 1
.....x ...... .....x ......     | 0  0  0  0  0   4 |  0  0  0   0  0  0  0  0   0   0  2  0  2  0 |  *  *  *  *  *  *  *   *  *  *  *  *  *  *  * 25  *  *  * |  0  0 0  0  0  0  1 1 0
.....x ...... ...... .....x     | 0  0  0  0  0   4 |  0  0  0   0  0  0  0  0   0   0  2  0  0  2 |  *  *  *  *  *  *  *   *  *  *  *  *  *  *  *  * 25  *  * |  0  0 0  1  0  0  0 0 1
...... .....x .....x ......     | 0  0  0  0  0   4 |  0  0  0   0  0  0  0  0   0   0  0  2  2  0 |  *  *  *  *  *  *  *   *  *  *  *  *  *  *  *  *  * 25  * |  0  0 0  0  1  0  0 1 0
...... .....x ...... .....x     | 0  0  0  0  0   4 |  0  0  0   0  0  0  0  0   0   0  0  2  0  2 |  *  *  *  *  *  *  *   *  *  *  *  *  *  *  *  *  *  * 25 |  0  0 0  0  0  1  0 0 1
--------------------------------+-------------------+----------------------------------------------+-----------------------------------------------------------+------------------------
o.x... ...... ...... o.x...&#x  ♦ 1  0  4  0  0   0 |  4  0  0   0  0  2  2  0   0   0  0  0  0  0 |  2  2  0  0  0  0  0   0  1  0  0  0  0  0  0  0  0  0  0 | 25  * *  *  *  *  * * *
...... ...... oxo...5oox...&#zx ♦ 1  5  5  0  0   0 |  5  0  5  10  0  0  5  0   0   0  0  0  0  0 |  0  5  0  1  5  5  0   0  0  0  0  0  0  0  0  0  0  0  0 |  * 10 *  *  *  *  * * * (tower: 132)
...... .x.... .x....5.o....     ♦ 0 10  0  0  0   0 |  0  5 10   0  0  0  0  0   0   0  0  0  0  0 |  0  0  5  2  0  0  0   0  0  0  0  0  0  0  0  0  0  0  0 |  *  * 5  *  *  *  * * *
.FxFox ...... ...... .oxofx&#zx ♦ 0  2  4  2  2   4 |  0  0  0   4  2  2  2  4   4   4  2  0  0  2 |  0  0  0  0  0  2  0   4  1  2  0  2  2  0  0  0  1  0  0 |  *  * * 25  *  *  * * * (tower: 32546)
...... .xFoFx .xofox ......&#xt ♦ 0  4  2  2  2   4 |  0  2  2   4  4  0  0  2   4   4  0  2  2  0 |  0  0  1  0  2  0  2   4  0  0  2  0  0  2  0  0  0  1  0 |  *  * *  * 25  *  * * * (tower: 23456)
...... ...o.x ...... ...o.x&#x  ♦ 0  0  0  1  0   4 |  0  0  0   0  0  0  0  0   4   0  0  2  0  2 |  0  0  0  0  0  0  0   0  0  0  2  2  0  0  0  0  0  0  1 |  *  * *  *  * 25  * * *
....ox ...... ....ox ......&#x  ♦ 0  0  0  0  1   4 |  0  0  0   0  0  0  0  0   0   4  2  0  2  0 |  0  0  0  0  0  0  0   0  0  0  0  0  2  2  0  1  0  0  0 |  *  * *  *  *  * 25 * *
.....x5.....x .....x ......     ♦ 0  0  0  0  0  20 |  0  0  0   0  0  0  0  0   0   0 10 10 10  0 |  0  0  0  0  0  0  0   0  0  0  0  0  0  0  2  5  0  5  0 |  *  * *  *  *  *  * 5 *
.....x5.....x ...... .....x     ♦ 0  0  0  0  0  20 |  0  0  0   0  0  0  0  0   0   0 10 10  0 10 |  0  0  0  0  0  0  0   0  0  0  0  0  0  0  2  0  5  0  5 |  *  * *  *  *  *  * * 5
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