Acronym cydadex
Name cyclical decadiminishing of ex
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
                   o5x                   
                                         
       x5o                     x5o       
                                         
                   f5o                   
            o5f           o5f            
                                         
o5x                                   o5x
       f5o                     f5o       
                                         
                   x5x                   
                                         
       o5f                     o5f       
x5o                                   x5o
                                         
            f5o           f5o            
                   o5f                   
                                         
       o5x                     o5x       
                                         
                   x5o                   
                 o5o           o5o                 
                        o5x                        
                                                   
            x5o                     x5o            
     o5o                                   o5o     
                        f5o                        
                 o5f           o5f                 
                                                   
     o5x                                   o5x     
            f5o                     f5o            
                                                   
o5o                                             o5o
                                                   
            o5f                     o5f            
     x5o                                   x5o     
                                                   
                 f5o           f5o                 
                        o5f                        
     o5o                                   o5o     
            o5x                     o5x            
                                                   
                        x5o                        
                 o5o           o5o                 
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between pap and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {5} between pap and pap:   144°
Confer
uniform relative:
ex   gap  
related CRFs:
Fxxox5ofxfo xofox5oxofx&#zx  

The great antiprism (gap) is a faceting of the hexacosachoron. The antiprism cells (pap) form 2 rings of 10 each. – This polychoron in contrast uses just a single such ring.


Incidence matrix according to Dynkin symbol

fooxo5ofxoo xofox5oxofx&#zx   → all existing heights = 0

o....5o.... o....5o....     | 25  *  *  *  * |  2   4  2  2  0  0  0  0   0  0  0  0 0 0 | 1  4  2  1  2   4   4   4 0  0  0   0  0  0  0  0   0  0  0 |  2  2  4  2   4  0  0  0  0  0
.o...5.o... .o...5.o...     |  * 25  *  *  * |  0   4  0  0  2  2  2  0   0  0  0  0 0 0 | 0  2  4  0  0   4   4   0 1  2  1   4  0  0  0  0   0  0  0 |  2  4  2  0   4  2  0  0  0  0
..o..5..o.. ..o..5..o..     |  *  * 25  *  *   0   0  2  0  0  2  0  2   4  2  0  0 0 0 | 0  0  0  2  0   4   0   4 0  1  0   4  2  4  4  1   4  0  0 |  0  2  0  4   4  2  2  4  2  0
...o.5...o. ...o.5...o.     |  *  *  * 25  *   0   0  0  2  0  0  2  0   4  0  2  2 0 0 | 0  0  0  0  1   0   4   4 0  0  2   4  4  2  0  0   4  4  1 |  0  0  2  2   4  4  4  2  0  2
....o5....o ....o5....o     |  *  *  *  * 10   0   0  0  0  0  0  0  0   0  5  0  5 1 1 | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  5  5  10  5  5 |  0  0  0  0   0  0  5  5  5  5
----------------------------+----------------+-------------------------------------------+-------------------------------------------------------------+-------------------------------
..... ..... x.... .....     |  2  0  0  0  0 | 25   *  *  *  *  *  *  *   *  *  *  * * * | 1  2  0  0  1   0   0   0 0  0  0   0  0  0  0  0   0  0  0 |  2  0  2  0   0  0  0  0  0  0
oo...5oo... oo...5oo...&#x  |  1  1  0  0  0 |  * 100  *  *  *  *  *  *   *  *  *  * * * | 0  1  1  0  0   1   1   0 0  0  0   0  0  0  0  0   0  0  0 |  1  1  1  0   1  0  0  0  0  0
o.o..5o.o.. o.o..5o.o..&#x  |  1  0  1  0  0 |  *   * 50  *  *  *  *  *   *  *  *  * * * | 0  0  0  1  0   2   0   2 0  0  0   0  0  0  0  0   0  0  0 |  0  1  0  2   2  0  0  0  0  0
o..o.5o..o. o..o.5o..o.&#x  |  1  0  0  1  0 |  *   *  * 50  *  *  *  *   *  *  *  * * * | 0  0  0  0  1   0   2   2 0  0  0   0  0  0  0  0   0  0  0 |  0  0  2  1   2  0  0  0  0  0
..... ..... ..... .x...     |  0  2  0  0  0 |  *   *  *  * 25  *  *  *   *  *  *  * * * | 0  0  2  0  0   0   0   0 1  1  0   0  0  0  0  0   0  0  0 |  2  2  0  0   0  0  0  0  0  0
.oo..5.oo.. .oo..5.oo..&#x  |  0  1  1  0  0 |  *   *  *  *  * 50  *  *   *  *  *  * * * | 0  0  0  0  0   2   0   0 0  1  0   2  0  0  0  0   0  0  0 |  0  2  0  0   2  1  0  0  0  0
.o.o.5.o.o. .o.o.5.o.o.&#x  |  0  1  0  1  0 |  *   *  *  *  *  * 50  *   *  *  *  * * * | 0  0  0  0  0   0   2   0 0  0  1   2  0  0  0  0   0  0  0 |  0  0  1  0   2  2  0  0  0  0
..... ..x.. ..... .....     |  0  0  2  0  0 |  *   *  *  *  *  *  * 25   *  *  *  * * * | 0  0  0  1  0   0   0   0 0  0  0   0  0  2  2  0   0  0  0 |  0  0  0  2   0  0  0  2  1  0
..oo.5..oo. ..oo.5..oo.&#x  |  0  0  1  1  0 |  *   *  *  *  *  *  *  * 100  *  *  * * * | 0  0  0  0  0   0   0   1 0  0  0   1  1  1  0  0   1  0  0 |  0  0  0  1   1  1  1  1  0  0
..o.o5..o.o ..o.o5..o.o&#x  |  0  0  1  0  1 |  *   *  *  *  *  *  *  *   * 50  *  * * * | 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  1  2  2  0
...x. ..... ..... .....     |  0  0  0  2  0 |  *   *  *  *  *  *  *  *   *  * 25  * * * | 0  0  0  0  0   0   0   0 0  0  1   0  2  0  0  0   0  2  0 |  0  0  0  0   0  2  2  0  0  1
...oo5...oo ...oo5...oo&#x  |  0  0  0  1  1 |  *   *  *  *  *  *  *  *   *  *  * 50 * * | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  0  0   2  2  1 |  0  0  0  0   0  0  2  1  0  2
..... ..... ....x .....     |  0  0  0  0  2 |  *   *  *  *  *  *  *  *   *  *  *  * 5 * | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  0  0   0  0  5 |  0  0  0  0   0  0  0  0  0  5
..... ..... ..... ....x     |  0  0  0  0  2 |  *   *  *  *  *  *  *  *   *  *  *  * * 5 | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  0  5   0  0  0 |  0  0  0  0   0  0  0  0  5  0
----------------------------+----------------+-------------------------------------------+-------------------------------------------------------------+-------------------------------
..... ..... x....5o....     |  5  0  0  0  0 |  5   0  0  0  0  0  0  0   0  0  0  0 0 0 | 5  *  *  *  *   *   *   * *  *  *   *  *  *  *  *   *  *  * |  2  0  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  0 0 0 | * 50  *  *  *   *   *   * *  *  *   *  *  *  *  *   *  *  * |  1  0  1  0   0  0  0  0  0  0
..... ..... ..... ox...&#x  |  1  2  0  0  0 |  0   2  0  0  1  0  0  0   0  0  0  0 0 0 | *  * 50  *  *   *   *   * *  *  *   *  *  *  *  *   *  *  * |  1  1  0  0   0  0  0  0  0  0
..... o.x.. ..... .....&#x  |  1  0  2  0  0 |  0   0  2  0  0  0  0  1   0  0  0  0 0 0 | *  *  * 25  *   *   *   * *  *  *   *  *  *  *  *   *  *  * |  0  0  0  2   0  0  0  0  0  0
..... ..... x..o. .....&#x  |  2  0  0  1  0 |  1   0  0  2  0  0  0  0   0  0  0  0 0 0 | *  *  *  * 25   *   *   * *  *  *   *  *  *  *  *   *  *  * |  0  0  2  0   0  0  0  0  0  0
ooo..5ooo.. ooo..5ooo..&#x  |  1  1  1  0  0 |  0   1  1  0  0  1  0  0   0  0  0  0 0 0 | *  *  *  *  * 100   *   * *  *  *   *  *  *  *  *   *  *  * |  0  1  0  0   1  0  0  0  0  0
oo.o.5oo.o. oo.o.5oo.o.&#x  |  1  1  0  1  0 |  0   1  0  1  0  0  1  0   0  0  0  0 0 0 | *  *  *  *  *   * 100   * *  *  *   *  *  *  *  *   *  *  * |  0  0  1  0   1  0  0  0  0  0
o.oo.5o.oo. o.oo.5o.oo.&#x  |  1  0  1  1  0 |  0   0  1  1  0  0  0  0   1  0  0  0 0 0 | *  *  *  *  *   *   * 100 *  *  *   *  *  *  *  *   *  *  * |  0  0  0  1   1  0  0  0  0  0
..... ..... .o...5.x...     |  0  5  0  0  0 |  0   0  0  0  5  0  0  0   0  0  0  0 0 0 | *  *  *  *  *   *   *   * 5  *  *   *  *  *  *  *   *  *  * |  2  0  0  0   0  0  0  0  0  0
..... ..... ..... .xo..&#x  |  0  2  1  0  0 |  0   0  0  0  1  2  0  0   0  0  0  0 0 0 | *  *  *  *  *   *   *   * * 25  *   *  *  *  *  *   *  *  * |  0  2  0  0   0  0  0  0  0  0
.o.x. ..... ..... .....&#x  |  0  1  0  2  0 |  0   0  0  0  0  0  2  0   0  0  1  0 0 0 | *  *  *  *  *   *   *   * *  * 25   *  *  *  *  *   *  *  * |  0  0  0  0   0  2  0  0  0  0
.ooo.5.ooo. .ooo.5.ooo.&#x  |  0  1  1  1  0 |  0   0  0  0  0  1  1  0   1  0  0  0 0 0 | *  *  *  *  *   *   *   * *  *  * 100  *  *  *  *   *  *  * |  0  0  0  0   1  1  0  0  0  0
..ox. ..... ..... .....&#x  |  0  0  1  2  0 |  0   0  0  0  0  0  0  0   2  0  1  0 0 0 | *  *  *  *  *   *   *   * *  *  *   * 50  *  *  *   *  *  * |  0  0  0  0   0  1  1  0  0  0
..... ..xo. ..... .....&#x  |  0  0  2  1  0 |  0   0  0  0  0  0  0  1   2  0  0  0 0 0 | *  *  *  *  *   *   *   * *  *  *   *  * 50  *  *   *  *  * |  0  0  0  1   0  0  0  1  0  0
..... ..x.o ..... .....&#x  |  0  0  2  0  1 |  0   0  0  0  0  0  0  1   0  2  0  0 0 0 | *  *  *  *  *   *   *   * *  *  *   *  *  * 50  *   *  *  * |  0  0  0  0   0  0  0  1  1  0
..... ..... ..... ..o.x&#x  |  0  0  1  0  2 |  0   0  0  0  0  0  0  0   0  2  0  0 0 1 | *  *  *  *  *   *   *   * *  *  *   *  *  *  * 25   *  *  * |  0  0  0  0   0  0  0  0  2  0
..ooo5..ooo ..ooo5..ooo&#x  |  0  0  1  1  1 |  0   0  0  0  0  0  0  0   1  1  0  1 0 0 | *  *  *  *  *   *   *   * *  *  *   *  *  *  *  * 100  *  * |  0  0  0  0   0  0  1  1  0  0
...xo ..... ..... .....&#x  |  0  0  0  2  1 |  0   0  0  0  0  0  0  0   0  0  1  2 0 0 | *  *  *  *  *   *   *   * *  *  *   *  *  *  *  *   * 50  * |  0  0  0  0   0  0  1  0  0  1
..... ..... ...ox .....&#x  |  0  0  0  1  2 |  0   0  0  0  0  0  0  0   0  0  0  2 1 0 | *  *  *  *  *   *   *   * *  *  *   *  *  *  *  *   *  * 25 |  0  0  0  0   0  0  0  0  0  2
----------------------------+----------------+-------------------------------------------+-------------------------------------------------------------+-------------------------------
..... ..... xo...5ox...&#x    5  5  0  0  0 |  5  10  0  0  5  0  0  0   0  0  0  0 0 0 | 1  5  5  0  0   0   0   0 1  0  0   0  0  0  0  0   0  0  0 | 10  *  *  *   *  *  *  *  *  *
..... ..... ..... oxo..&#x    1  2  1  0  0 |  0   2  1  0  1  2  0  0   0  0  0  0 0 0 | 0  0  1  0  0   2   0   0 0  1  0   0  0  0  0  0   0  0  0 |  * 50  *  *   *  *  *  *  *  *
..... ..... xo.o. .....&#x    2  1  0  1  0 |  1   2  0  2  0  0  1  0   0  0  0  0 0 0 | 0  1  0  0  1   0   2   0 0  0  0   0  0  0  0  0   0  0  0 |  *  * 50  *   *  *  *  *  *  *
..... o.xo. ..... .....&#x    1  0  2  1  0 |  0   0  2  1  0  0  0  1   2  0  0  0 0 0 | 0  0  0  1  0   0   0   2 0  0  0   0  0  1  0  0   0  0  0 |  *  *  * 50   *  *  *  *  *  *
oooo.5oooo. oooo.5oooo.&#x    1  1  1  1  0 |  0   1  1  1  0  1  1  0   1  0  0  0 0 0 | 0  0  0  0  0   1   1   1 0  0  0   1  0  0  0  0   0  0  0 |  *  *  *  * 100  *  *  *  *  *
.oox. ..... ..... .....&#x    0  1  1  2  0 |  0   0  0  0  0  1  2  0   2  0  1  0 0 0 | 0  0  0  0  0   0   0   0 0  0  1   2  1  0  0  0   0  0  0 |  *  *  *  *   * 50  *  *  *  *
..oxo ..... ..... .....&#x    0  0  1  2  1 |  0   0  0  0  0  0  0  0   2  1  1  2 0 0 | 0  0  0  0  0   0   0   0 0  0  0   0  1  0  0  0   2  1  0 |  *  *  *  *   *  * 50  *  *  *
..... ..xoo ..... .....&#x    0  0  2  1  1 |  0   0  0  0  0  0  0  1   2  2  0  1 0 0 | 0  0  0  0  0   0   0   0 0  0  0   0  0  1  1  0   2  0  0 |  *  *  *  *   *  *  * 50  *  *
..... ..x.o ..... ..o.x&#x    0  0  2  0  2 |  0   0  0  0  0  0  0  1   0  4  0  0 0 1 | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  2  2   0  0  0 |  *  *  *  *   *  *  *  * 25  *
...xo ..... ...ox .....&#x    0  0  0  2  2 |  0   0  0  0  0  0  0  0   0  0  1  4 1 0 | 0  0  0  0  0   0   0   0 0  0  0   0  0  0  0  0   0  2  2 |  *  *  *  *   *  *  *  *  * 25

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