Acronym ...
Name vertex-first rotunda of hexacosachoron
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
                 o5o       
                        o5x
                           
            x5o            
     o5o                   
                        f5o
                 o5f       
                           
     o5x                   
            f5o            
                           
o5o                     x5x
                           
            o5f            
     x5o                   
                           
                 f5o       
                        o5f
     o5o                   
            o5x            
                           
                        x5o
                 o5o       
                o3o                
                                   
        x3o   o3f f3o   o3x            (F=ff)
                                   
                                   
 o3o o3f   f3x       x3f   f3o o3o 
                                   
   f3o       o3F   F3o       o3f   
                                   
                                   
o3x   x3f F3o   f3f   o3F f3x   x3o
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between peppy and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {5} between id and peppy:   108°
  • at {3} between id and tet:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
Confer
segmentochora:
ikepy   ike || doe   doe || id  
other CRFs:
1/10-luna of ex   2/10-luna of ex   3/10-luna of ex   4/10-luna of ex   pt || ike || doe || id   ike || doe || id   ike || doe || f-ike || id   ike || f-ike || id  
uniform relative:
ex  

Incidence matrix according to Dynkin symbol

oxofo3oooox5ooxoo&#xt   → height(1,2) = height(3,4) = (sqrt(5)-1)/4 = 0.309017
                                      height(2,3) = height(4,5) = 1/2
(pt || pseudo ike || pseudo doe || pseudo f-ike || id)

o....3o....5o....     | 1  *  *  *  *  12  0  0  0  0  0  0  0  0 | 30  0  0  0  0  0  0  0   0  0  0  0 | 20  0  0  0  0  0  0  0 0
.o...3.o...5.o...     | * 12  *  *  *   1  5  5  1  0  0  0  0  0 |  5  5 10  5  5  0  0  0   0  0  0  0 |  5  5  5  5  0  0  0  0 0
..o..3..o..5..o..     | *  * 20  *  *   0  0  3  0  3  3  3  0  0 |  0  0  3  6  3  6  3  3   6  0  0  0 |  0  1  3  6  1  3  6  0 0
...o.3...o.5...o.     | *  *  * 12  *   0  0  0  1  0  5  0  5  0 |  0  0  0  0  5  5  0  0  10  5  0  0 |  0  0  0  5  0  5  5  1 0
....o3....o5....o     | *  *  *  * 30 |  0  0  0  0  0  0  2  2  4 |  0  0  0  0  0  0  4  1   4  4  2  2 |  0  0  0  0  2  4  2  2 1
----------------------+---------------+----------------------------+--------------------------------------+--------------------------
oo...3oo...5oo...&#x  | 1  1  0  0  0 | 12  *  *  *  *  *  *  *  * |  5  0  0  0  0  0  0  0   0  0  0  0 |  5  0  0  0  0  0  0  0 0
.x... ..... .....     | 0  2  0  0  0 |  * 30  *  *  *  *  *  *  * |  1  2  2  0  0  0  0  0   0  0  0  0 |  2  2  1  0  0  0  0  0 0
.oo..3.oo..5.oo..&#x  | 0  1  1  0  0 |  *  * 60  *  *  *  *  *  * |  0  0  2  2  1  0  0  0   0  0  0  0 |  0  1  2  2  0  0  0  0 0
.o.o.3.o.o.5.o.o.&#x  | 0  1  0  1  0 |  *  *  * 12  *  *  *  *  * |  0  0  0  0  5  0  0  0   0  0  0  0 |  0  0  0  5  0  0  0  0 0
..... ..... ..x..     | 0  0  2  0  0 |  *  *  *  * 30  *  *  *  * |  0  0  0  2  0  2  0  1   0  0  0  0 |  0  0  1  2  0  0  2  0 0
..oo.3..oo.5..oo.&#x  | 0  0  1  1  0 |  *  *  *  *  * 60  *  *  * |  0  0  0  0  1  2  0  0   2  0  0  0 |  0  0  0  2  0  1  2  0 0
..o.o3..o.o5..o.o&#x  | 0  0  1  0  1 |  *  *  *  *  *  * 60  *  * |  0  0  0  0  0  0  2  1   2  0  0  0 |  0  0  0  0  1  2  2  0 0
...oo3...oo5...oo&#x  | 0  0  0  1  1 |  *  *  *  *  *  *  * 60  * |  0  0  0  0  0  0  0  0   2  2  0  0 |  0  0  0  0  0  2  1  1 0
..... ....x .....     | 0  0  0  0  2 |  *  *  *  *  *  *  *  * 60 |  0  0  0  0  0  0  1  0   0  1  1  1 |  0  0  0  0  1  1  0  1 1
----------------------+---------------+----------------------------+--------------------------------------+--------------------------
ox... ..... .....&#x  | 1  2  0  0  0 |  2  1  0  0  0  0  0  0  0 | 30  *  *  *  *  *  *  *   *  *  *  * |  2  0  0  0  0  0  0  0 0
.x...3.o... .....     | 0  3  0  0  0 |  0  3  0  0  0  0  0  0  0 |  * 20  *  *  *  *  *  *   *  *  *  * |  1  1  0  0  0  0  0  0 0
.xo.. ..... .....&#x  | 0  2  1  0  0 |  0  1  2  0  0  0  0  0  0 |  *  * 60  *  *  *  *  *   *  *  *  * |  0  1  1  0  0  0  0  0 0
..... ..... .ox..&#x  | 0  1  2  0  0 |  0  0  2  0  1  0  0  0  0 |  *  *  * 60  *  *  *  *   *  *  *  * |  0  0  1  1  0  0  0  0 0
.ooo.3.ooo.5.ooo.&#x  | 0  1  1  1  0 |  0  0  1  1  0  1  0  0  0 |  *  *  *  * 60  *  *  *   *  *  *  * |  0  0  0  2  0  0  0  0 0
..... ..... ..xo.&#x  | 0  0  2  1  0 |  0  0  0  0  1  2  0  0  0 |  *  *  *  *  * 60  *  *   *  *  *  * |  0  0  0  1  0  0  1  0 0
..... ..o.x .....&#x  | 0  0  1  0  2 |  0  0  0  0  0  0  2  0  1 |  *  *  *  *  *  * 60  *   *  *  *  * |  0  0  0  0  1  1  0  0 0
..... ..... ..x.o&#x  | 0  0  2  0  1 |  0  0  0  0  1  0  2  0  0 |  *  *  *  *  *  *  * 30   *  *  *  * |  0  0  0  0  0  0  2  0 0
..ooo3..ooo5..ooo&#x  | 0  0  1  1  1 |  0  0  0  0  0  1  1  1  0 |  *  *  *  *  *  *  *  * 120  *  *  * |  0  0  0  0  0  1  1  0 0
..... ...ox .....&#x  | 0  0  0  1  2 |  0  0  0  0  0  0  0  2  1 |  *  *  *  *  *  *  *  *   * 60  *  * |  0  0  0  0  0  1  0  1 0
....o3....x .....     | 0  0  0  0  3 |  0  0  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *   *  * 20  * |  0  0  0  0  1  0  0  0 1
..... ....x5....o     | 0  0  0  0  5 |  0  0  0  0  0  0  0  0  5 |  *  *  *  *  *  *  *  *   *  *  * 12 |  0  0  0  0  0  0  0  1 1
----------------------+---------------+----------------------------+--------------------------------------+--------------------------
ox...3oo... .....&#x   1  3  0  0  0 |  3  3  0  0  0  0  0  0  0 |  3  1  0  0  0  0  0  0   0  0  0  0 | 20  *  *  *  *  *  *  * *
.xo..3.oo.. .....&#x   0  3  1  0  0 |  0  3  3  0  0  0  0  0  0 |  0  1  3  0  0  0  0  0   0  0  0  0 |  * 20  *  *  *  *  *  * *
.xo.. ..... .ox..&#x   0  2  2  0  0 |  0  1  4  0  1  0  0  0  0 |  0  0  2  2  0  0  0  0   0  0  0  0 |  *  * 30  *  *  *  *  * *
..... ..... .oxo.&#xt  0  1  2  1  0 |  0  0  2  1  1  2  0  0  0 |  0  0  0  1  2  1  0  0   0  0  0  0 |  *  *  * 60  *  *  *  * *
..o.o3..o.x .....&#x   0  0  1  0  3 |  0  0  0  0  0  0  3  0  3 |  0  0  0  0  0  0  3  0   0  0  1  0 |  *  *  *  * 20  *  *  * *
..... ..oox .....&#xt  0  0  1  1  2 |  0  0  0  0  0  1  2  2  1 |  0  0  0  0  0  0  1  0   2  1  0  0 |  *  *  *  *  * 60  *  * *
..... ..... ..xoo&#xt  0  0  2  1  1 |  0  0  0  0  1  2  2  1  0 |  0  0  0  0  0  1  0  1   2  0  0  0 |  *  *  *  *  *  * 60  * *
..... ...ox5...oo&#x   0  0  0  1  5 |  0  0  0  0  0  0  0  5  5 |  0  0  0  0  0  0  0  0   0  5  0  1 |  *  *  *  *  *  *  * 12 *
....o3....x5....o      0  0  0  0 30 |  0  0  0  0  0  0  0  0 60 |  0  0  0  0  0  0  0  0   0  0 20 12 |  *  *  *  *  *  *  *  * 1

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