Acronym ...
Name triacontapenta-diminished hexacosachoron,
fooo5ofxo xofx5oxox&#zx
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
                 o5o           o5o                 
                        o5x    D                   
                        C                          
                                                   
     o5o                                   o5o     
                        f5o                        
                 o5f    A      o5f                 
                               B                   
     o5x                                   o5x     
            f5o                     f5o            
                                                   
o5o                                             o5o
                                                   
            o5f                     o5f            
                                                   
                                                   
                 f5o           f5o                 
                        o5f                        
     o5o                                   o5o     
            o5x                     o5x            
                                                   
                                                   
                 o5o           o5o                 
                   x5o                   
                   A                     
       o5x                     o5x       
                               B         
                                         
            f5o           f5o            
                          C              
x5o                                   x5o
                                         
                                         
                   x5x                   
                   D                     
       f5o                     f5o       
o5x                                   o5x
                                         
                                         
                   f5o                   
                                         
       x5o                     x5o       
                                         
                   o5x                   
Confer
uniform relatives:
ex   gap  
related CRFs:
Fxxx5ofxo xofx5oxox&#zx   xfooo5xofxo oxofx5ooxox&#zx  

This orbiform CRF polychoron can be derived as a triacontapenta-diminishing of ex: In fact ex wrt. its pedipic subsymmetry I2(5)×I2(5) is given as xfooxo5xofxoo oxofox5ooxofx&#zx. While gap was derived therefrom by deleting the first and last layer this one is obtained by deleting the first and the fifth layer instead. Thus, depending on the chosen respective projection, there are 2 different according lace cities here.

Note that the deletion of first and fourth layer would result in the same figure. And that the deletion of the first and second and (alike again) the first and third layer would result in non-CRF polychora. Thence the naming as the triacontapenta-diminished hexacosachoron seems to be appropriate.

A diminishing in solely the fifth layer would result in xfooo5xofxo oxofx5ooxox&#zx.

This polychoron also allows for a Stott expansion wrt. the first node, then resulting in Fxxx5ofxo xofx5oxox&#zx.


Incidence matrix according to Dynkin symbol

fooo5ofxo xofx5oxox&#zx   → height = 0

o...5o... o...5o...     | 25  *  *  * |  2   4  2  0  0  0  0 0 0 | 1  4  2   4  1 0  0  0  0  0 |  2  2  2  0  A
.o..5.o.. .o..5.o..     |  * 25  *  * |  0   4  0  2  2  0  0 0 0 | 0  2  4   4  0 1  2  1  0  0 |  2  4  2  0  B
..o.5..o. ..o.5..o.     |  *  * 25  * |  0   0  2  0  2  2  2 0 0 | 0  0  0   4  2 0  1  2  4  1 |  0  2  4  2  C
...o5...o ...o5...o     |  *  *  * 10 |  0   0  0  0  0  0  5 1 1 | 0  0  0   0  0 0  0  5  5  5 |  0  0  5  5  D
------------------------+-------------+---------------------------+------------------------------+------------
.... .... x... ....     |  2  0  0  0 | 25   *  *  *  *  *  * * * | 1  2  0   0  0 0  0  0  0  0 |  2  0  1  0
oo..5oo.. oo..5oo..&#x  |  1  1  0  0 |  * 100  *  *  *  *  * * * | 0  1  1   1  0 0  0  0  0  0 |  1  1  1  0
o.o.5o.o. o.o.5o.o.&#x  |  1  0  1  0 |  *   * 50  *  *  *  * * * | 0  0  0   2  1 0  0  0  0  0 |  0  1  2  0
.... .... .... .x..     |  0  2  0  0 |  *   *  * 25  *  *  * * * | 0  0  2   0  0 1  1  0  0  0 |  2  2  0  0
.oo.5.oo. .oo.5.oo.&#x  |  0  1  1  0 |  *   *  *  * 50  *  * * * | 0  0  0   2  0 0  1  1  0  0 |  0  2  2  0
.... ..x. .... ....     |  0  0  2  0 |  *   *  *  *  * 25  * * * | 0  0  0   0  1 0  0  0  2  0 |  0  0  2  1
..oo5..oo ..oo5..oo&#x  |  0  0  1  1 |  *   *  *  *  *  * 50 * * | 0  0  0   0  0 0  0  1  2  1 |  0  0  2  2
.... .... ...x ....     |  0  0  0  2 |  *   *  *  *  *  *  * 5 * | 0  0  0   0  0 0  0  5  0  0 |  0  0  5  0
.... .... .... ...x     |  0  0  0  2 |  *   *  *  *  *  *  * * 5 | 0  0  0   0  0 0  0  0  0  5 |  0  0  0  5
------------------------+-------------+---------------------------+------------------------------+------------
.... .... x...5o...     |  5  0  0  0 |  5   0  0  0  0  0  0 0 0 | 5  *  *   *  * *  *  *  *  * |  2  0  0  0
.... .... xo.. ....&#x  |  2  1  0  0 |  1   2  0  0  0  0  0 0 0 | * 50  *   *  * *  *  *  *  * |  1  0  1  0
.... .... .... ox..&#x  |  1  2  0  0 |  0   2  0  1  0  0  0 0 0 | *  * 50   *  * *  *  *  *  * |  1  1  0  0
ooo.5ooo. ooo.5ooo.&#x  |  1  1  1  0 |  0   1  1  0  1  0  0 0 0 | *  *  * 100  * *  *  *  *  * |  0  1  1  0
.... o.x. .... ....&#x  |  1  0  2  0 |  0   0  2  0  0  1  0 0 0 | *  *  *   * 25 *  *  *  *  * |  0  0  2  0
.... .... .o..5.x..     |  0  5  0  0 |  0   0  0  5  0  0  0 0 0 | *  *  *   *  * 5  *  *  *  * |  2  0  0  0
.... .... .... .xo.&#x  |  0  2  1  0 |  0   0  0  1  2  0  0 0 0 | *  *  *   *  * * 25  *  *  * |  0  2  0  0
.... .... .ofx ....&#xt |  0  1  2  2 |  0   0  0  0  2  0  2 1 0 | *  *  *   *  * *  * 25  *  * |  0  0  2  0
.... ..xo .... ....&#x  |  0  0  2  1 |  0   0  0  0  0  1  2 0 0 | *  *  *   *  * *  *  * 50  * |  0  0  1  1
.... .... .... ..ox&#x  |  0  0  1  2 |  0   0  0  0  0  0  2 0 1 | *  *  *   *  * *  *  *  * 25 |  0  0  0  2
------------------------+-------------+---------------------------+------------------------------+------------
.... .... xo..5ox..&#x    5  5  0  0 |  5  10  0  5  0  0  0 0 0 | 1  5  5   0  0 1  0  0  0  0 | 10  *  *  *
.... .... .... oxo.&#x    1  2  1  0 |  0   2  1  1  2  0  0 0 0 | 0  0  1   2  0 0  1  0  0  0 |  * 50  *  *
.... ofxo xofx ....&#xt   2  2  4  2 |  1   4  4  0  4  2  4 1 0 | 0  2  0   4  2 0  0  2  2  0 |  *  * 25  *
.... ..xo .... ..ox&#x    0  0  2  2 |  0   0  0  0  0  1  4 0 1 | 0  0  0   0  0 0  0  0  2  2 |  *  *  * 25

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