Acronym ...
Name oFFxx3xxoxf3Fxxox3oofFx&#zx
Confer
uniform relative:
ex  
general polytopal classes:
expanded kaleido-facetings  

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 ..... .....&#zx |  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

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