Acronym ...
Name xFfoo3xoxxF3fxoxo3ooffx&#zx
Confer
uniform relative:
ex  
related CRFs:
oFFxx3xxoof3fooxo3ooffx&#zx  
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 xFfoo3o(-x)oof3fxoxo3ooffx&#zx. Then a Stott expansion wrt. the second 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

xFfoo3xoxxF3fxoxo3ooffx&#zx   → all heights = 0 – except those of the not existing lacing(2,4) resp. lacing(2,5).

o....3o....3o....3o....     | 60  *  *  *  * |  1  1  1   2   2   2  0   0  0   0  0  0  0  0  0 |  1  1  2  2  2  2  1   2   2   2   2  0  0  0  0  0  0  0   0  0  0  0  0 |  2  1  2  2  1  2   2 0  0  0  0 0
.o...3.o...3.o...3.o...     |  * 30  *  *  * |  0  0  2   0   0   0  4   4  0   0  0  0  0  0  0 |  0  1  0  0  0  0  0   4   0   0   0  2  2  2  4  0  0  0   0  0  0  0  0 |  0  0  0  2  2  0   0 1  2  0  0 0
..o..3..o..3..o..3..o..     |  *  * 60  *  * |  0  0  0   2   0   0  0   2  2   2  1  0  0  0  0 |  0  0  2  0  0  0  0   2   2   2   0  0  0  2  1  1  2  1   2  0  0  0  0 |  0  0  0  2  1  2   2 0  1  1  1 0
...o.3...o.3...o.3...o.     |  *  *  * 60  * |  0  0  0   0   2   0  0   0  0   2  0  2  1  1  0 |  0  0  0  1  2  0  0   0   2   0   2  0  0  0  0  0  2  2   2  1  2  1  0 |  1  0  1  0  0  2   2 0  0  2  2 1
....o3....o3....o3....o     |  *  *  *  * 30 |  0  0  0   0   0   4  0   0  0   0  2  0  0  2  2 |  0  0  0  0  0  2  4   0   0   4   4  0  0  0  0  0  0  0   4  0  0  1  1 |  0  2  2  0  2  0   4 0  0  0  2 0
----------------------------+----------------+---------------------------------------------------+---------------------------------------------------------------------------+-----------------------------------
x.... ..... ..... .....     |  2  0  0  0  0 | 30  *  *   *   *   *  *   *  *   *  *  *  *  *  * |  1  0  0  2  0  2  0   0   0   0   0  0  0  0  0  0  0  0   0  0  0  0  0 |  2  1  2  0  0  0   0 0  0  0  0 0
..... x.... ..... .....     |  2  0  0  0  0 |  * 30  *   *   *   *  *   *  *   *  *  *  *  *  * |  1  1  2  0  2  0  0   0   0   0   0  0  0  0  0  0  0  0   0  0  0  0  0 |  2  0  0  2  0  2   0 0  0  0  0 0
oo...3oo...3oo...3oo...&#x  |  1  1  0  0  0 |  *  * 60   *   *   *  *   *  *   *  *  *  *  *  * |  0  1  0  0  0  0  0   2   0   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
o.o..3o.o..3o.o..3o.o..&#x  |  1  0  1  0  0 |  *  *  * 120   *   *  *   *  *   *  *  *  *  *  * |  0  0  1  0  0  0  0   1   1   1   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
o..o.3o..o.3o..o.3o..o.&#x  |  1  0  0  1  0 |  *  *  *   * 120   *  *   *  *   *  *  *  *  *  * |  0  0  0  1  1  0  0   0   1   0   1  0  0  0  0  0  0  0   0  0  0  0  0 |  1  0  1  0  0  1   1 0  0  0  0 0
o...o3o...o3o...o3o...o&#x  |  1  0  0  0  1 |  *  *  *   *   * 120  *   *  *   *  *  *  *  *  * |  0  0  0  0  0  1  1   0   0   1   1  0  0  0  0  0  0  0   0  0  0  0  0 |  0  1  1  0  1  0   1 0  0  0  0 0
..... ..... .x... .....     |  0  2  0  0  0 |  *  *  *   *   *   * 60   *  *   *  *  *  *  *  * |  0  0  0  0  0  0  0   0   0   0   0  1  1  0  1  0  0  0   0  0  0  0  0 |  0  0  0  0  1  0   0 1  1  0  0 0
.oo..3.oo..3.oo..3.oo..&#x  |  0  1  1  0  0 |  *  *  *   *   *   *  * 120  *   *  *  *  *  *  * |  0  0  0  0  0  0  0   1   0   0   0  0  0  1  1  0  0  0   0  0  0  0  0 |  0  0  0  1  1  0   0 0  1  0  0 0
..... ..x.. ..... .....     |  0  0  2  0  0 |  *  *  *   *   *   *  *   * 60   *  *  *  *  *  * |  0  0  1  0  0  0  0   0   0   0   0  0  0  1  0  1  1  0   0  0  0  0  0 |  0  0  0  1  0  1   0 0  1  1  0 0
..oo.3..oo.3..oo.3..oo.&#x  |  0  0  1  1  0 |  *  *  *   *   *   *  *   *  * 120  *  *  *  *  * |  0  0  0  0  0  0  0   0   1   0   0  0  0  0  0  0  1  1   1  0  0  0  0 |  0  0  0  0  0  1   1 0  0  1  1 0
..o.o3..o.o3..o.o3..o.o&#x  |  0  0  1  0  1 |  *  *  *   *   *   *  *   *  *   * 60  *  *  *  * |  0  0  0  0  0  0  0   0   0   2   0  0  0  0  0  0  0  0   2  0  0  0  0 |  0  0  0  0  1  0   2 0  0  0  1 0
..... ...x. ..... .....     |  0  0  0  2  0 |  *  *  *   *   *   *  *   *  *   *  * 60  *  *  * |  0  0  0  0  1  0  0   0   0   0   0  0  0  0  0  0  1  0   0  1  1  0  0 |  1  0  0  0  0  1   0 0  0  1  0 1
..... ..... ...x. .....     |  0  0  0  2  0 |  *  *  *   *   *   *  *   *  *   *  *  * 30  *  * |  0  0  0  0  0  0  0   0   0   0   0  0  0  0  0  0  0  2   0  0  2  1  0 |  0  0  0  0  0  0   0 0  0  2  2 1
...oo3...oo3...oo3...oo&#x  |  0  0  0  1  1 |  *  *  *   *   *   *  *   *  *   *  *  *  * 60  * |  0  0  0  0  0  0  0   0   0   0   2  0  0  0  0  0  0  0   2  0  0  1  0 |  0  0  1  0  0  0   2 0  0  0  2 0
..... ..... ..... ....x     |  0  0  0  0  2 |  *  *  *   *   *   *  *   *  *   *  *  *  *  * 30 |  0  0  0  0  0  0  2   0   0   0   0  0  0  0  0  0  0  0   0  0  0  0  1 |  0  1  0  0  2  0   0 0  0  0  0 0
----------------------------+----------------+---------------------------------------------------+---------------------------------------------------------------------------+-----------------------------------
x....3x.... ..... .....     |  6  0  0  0  0 |  3  3  0   0   0   0  0   0  0   0  0  0  0  0  0 | 10  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  2  0  0  0  0  0   0 0  0  0  0 0
..... xo... ..... .....&#x  |  2  1  0  0  0 |  0  1  2   0   0   0  0   0  0   0  0  0  0  0  0 |  * 30  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  2  0  0   0 0  0  0  0 0
..... x.x.. ..... .....&#x  |  2  0  2  0  0 |  0  1  0   2   0   0  0   0  1   0  0  0  0  0  0 |  *  * 60  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  1  0  1   0 0  0  0  0 0
x..o. ..... ..... .....&#x  |  2  0  0  1  0 |  1  0  0   0   2   0  0   0  0   0  0  0  0  0  0 |  *  *  * 60  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  1  0  1  0  0  0   0 0  0  0  0 0
..... x..x. ..... .....&#x  |  2  0  0  2  0 |  0  1  0   0   2   0  0   0  0   0  0  1  0  0  0 |  *  *  *  * 60  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  1  0  0  0  0  1   0 0  0  0  0 0
x...o ..... ..... .....&#x  |  2  0  0  0  1 |  1  0  0   0   0   2  0   0  0   0  0  0  0  0  0 |  *  *  *  *  * 60  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  1  1  0  0  0   0 0  0  0  0 0
..... ..... ..... o...x&#x  |  1  0  0  0  2 |  0  0  0   0   0   2  0   0  0   0  0  0  0  0  1 |  *  *  *  *  *  * 60   *   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  1  0  0  1  0   0 0  0  0  0 0
ooo..3ooo..3ooo..3ooo..&#x  |  1  1  1  0  0 |  0  0  1   1   0   0  0   1  0   0  0  0  0  0  0 |  *  *  *  *  *  *  * 120   *   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  1  1  0   0 0  0  0  0 0
o.oo.3o.oo.3o.oo.3o.oo.&#x  |  1  0  1  1  0 |  0  0  0   1   1   0  0   0  0   1  0  0  0  0  0 |  *  *  *  *  *  *  *   * 120   *   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  0  0  1   1 0  0  0  0 0
o.o.o3o.o.o3o.o.o3o.o.o&#x  |  1  0  1  0  1 |  0  0  0   1   0   1  0   0  0   0  1  0  0  0  0 |  *  *  *  *  *  *  *   *   * 120   *  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  0  1  0   1 0  0  0  0 0
o..oo3o..oo3o..oo3o..oo&#x  |  1  0  0  1  1 |  0  0  0   0   1   1  0   0  0   0  0  0  0  1  0 |  *  *  *  *  *  *  *   *   *   * 120  *  *  *  *  *  *  *   *  *  *  *  * |  0  0  1  0  0  0   1 0  0  0  0 0
..... .o...3.x... .....     |  0  3  0  0  0 |  0  0  0   0   0   0  3   0  0   0  0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   *   * 20  *  *  *  *  *  *   *  *  *  *  * |  0  0  0  0  0  0   0 1  1  0  0 0
..... ..... .x...3.o...     |  0  3  0  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  1  2  0  0 |  0  0  0   0   0   0  0   2  1   0  0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  * 60  *  *  *  *   *  *  *  *  * |  0  0  0  1  0  0   0 0  1  0  0 0
..... ..... .xo.. .....&#x  |  0  2  1  0  0 |  0  0  0   0   0   0  1   2  0   0  0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  * 60  *  *  *   *  *  *  *  * |  0  0  0  0  1  0   0 0  1  0  0 0
..... ..x..3..o.. .....     |  0  0  3  0  0 |  0  0  0   0   0   0  0   0  3   0  0  0  0  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  * 20  *  *   *  *  *  *  * |  0  0  0  0  0  0   0 0  1  1  0 0
..... ..xx. ..... .....&#x  |  0  0  2  2  0 |  0  0  0   0   0   0  0   0  1   2  0  1  0  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  * 60  *   *  *  *  *  * |  0  0  0  0  0  1   0 0  0  1  0 0
..... ..... ..ox. .....&#x  |  0  0  1  2  0 |  0  0  0   0   0   0  0   0  0   2  0  0  1  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  * 60   *  *  *  *  * |  0  0  0  0  0  0   0 0  0  1  1 0
..ooo3..ooo3..ooo3..ooo&#x  |  0  0  1  1  1 |  0  0  0   0   0   0  0   0  0   1  1  0  0  1  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  * 120  *  *  *  * |  0  0  0  0  0  0   1 0  0  0  1 0
...o.3...x. ..... .....     |  0  0  0  3  0 |  0  0  0   0   0   0  0   0  0   0  0  3  0  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   * 20  *  *  * |  1  0  0  0  0  0   0 0  0  0  0 1
..... ...x.3...x. .....     |  0  0  0  6  0 |  0  0  0   0   0   0  0   0  0   0  0  3  3  0  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  * 20  *  * |  0  0  0  0  0  0   0 0  0  1  0 1
..... ..... ...xo .....&#x  |  0  0  0  2  1 |  0  0  0   0   0   0  0   0  0   0  0  0  1  2  0 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  * 30  * |  0  0  0  0  0  0   0 0  0  0  2 0
..... ..... ....o3....x     |  0  0  0  0  3 |  0  0  0   0   0   0  0   0  0   0  0  0  0  0  3 |  *  *  *  *  *  *  *   *   *   *   *  *  *  *  *  *  *  *   *  *  *  * 10 |  0  0  0  0  2  0   0 0  0  0  0 0
----------------------------+----------------+---------------------------------------------------+---------------------------------------------------------------------------+-----------------------------------
x..o.3x..x. ..... .....&#x    6  0  0  3  0 |  3  3  0   0   6   0  0   0  0   0  0  3  0  0  0 |  1  0  0  3  3  0  0   0   0   0   0  0  0  0  0  0  0  0   0  1  0  0  0 | 20  *  *  *  *  *   * *  *  *  * *
x...o ..... ..... o...x&#x    2  0  0  0  2 |  1  0  0   0   0   4  0   0  0   0  0  0  0  0  1 |  0  0  0  0  0  2  2   0   0   0   0  0  0  0  0  0  0  0   0  0  0  0  0 |  * 30  *  *  *  *   * *  *  *  * *
x..oo ..... ..... .....&#x    2  0  0  1  1 |  1  0  0   0   2   2  0   0  0   0  0  0  0  1  0 |  0  0  0  1  0  1  0   0   0   0   2  0  0  0  0  0  0  0   0  0  0  0  0 |  *  * 60  *  *  *   * *  *  *  * *
..... xox.. ..... .....&#x    2  1  2  0  0 |  0  1  2   2   0   0  0   2  1   0  0  0  0  0  0 |  0  1  1  0  0  0  0   2   0   0   0  0  0  1  0  0  0  0   0  0  0  0  0 |  *  *  * 60  *  *   * *  *  *  * *
..... ..... fxo.o3oof.x&#zx   3  3  3  0  3 |  0  0  3   6   0   6  3   6  0   0  3  0  0  0  3 |  0  0  0  0  0  0  3   6   0   6   0  0  1  0  3  0  0  0   0  0  0  0  1 |  *  *  *  * 20  *   * *  *  *  * *
..... x.xx. ..... .....&#x    2  0  2  2  0 |  0  1  0   2   2   0  0   0  1   2  0  1  0  0  0 |  0  0  1  0  1  0  0   0   2   0   0  0  0  0  0  0  1  0   0  0  0  0  0 |  *  *  *  *  * 60   * *  *  *  * *
o.ooo3o.ooo3o.ooo3o.ooo&#x    1  0  1  1  1 |  0  0  0   1   1   1  0   0  0   1  1  0  0  1  0 |  0  0  0  0  0  0  0   0   1   1   1  0  0  0  0  0  0  0   1  0  0  0  0 |  *  *  *  *  *  * 120 *  *  *  * *
..... .o...3.x...3.o...       0  6  0  0  0 |  0  0  0   0   0   0 12   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   0  0  0  0  0 |  *  *  *  *  *  *   * 5  *  *  * *
..... .ox..3.xo.. .....&#x    0  3  3  0  0 |  0  0  0   0   0   0  3   6  3   0  0  0  0  0  0 |  0  0  0  0  0  0  0   0   0   0   0  1  0  3  3  1  0  0   0  0  0  0  0 |  *  *  *  *  *  *   * * 20  *  * *
..... ..xx.3..ox. .....&#x    0  0  3  6  0 |  0  0  0   0   0   0  0   0  3   6  0  3  3  0  0 |  0  0  0  0  0  0  0   0   0   0   0  0  0  0  0  1  3  3   0  0  1  0  0 |  *  *  *  *  *  *   * *  * 20  * *
..... ..... ..oxo .....&#x    0  0  1  2  1 |  0  0  0   0   0   0  0   0  0   2  1  0  1  2  0 |  0  0  0  0  0  0  0   0   0   0   0  0  0  0  0  0  0  1   2  0  0  1  0 |  *  *  *  *  *  *   * *  *  * 60 *
...o.3...x.3...x. .....       0  0  0 12  0 |  0  0  0   0   0   0  0   0  0   0  0 12  6  0  0 |  0  0  0  0  0  0  0   0   0   0   0  0  0  0  0  0  0  0   0  4  4  0  0 |  *  *  *  *  *  *   * *  *  *  * 5

© 2004-2018
top of page