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°
Face vector 75, 384, 592, 283
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   pesc  
uniform relative:
ex  

The upper lace city above shows that this polychoron is not exactly half of ex: rather, if attaching its mirror image onto the right, it can be seen at the top and bottom that pentagonal scalene dimples in here got omitted, which elsewise would had got dissected midwise. In fact there would be 12 such pescs all around on that mirror hyper plane. Despite this lack this rotunda in here still is convex, as is proven by the given dihedral angles. Even more, this rotunda indeed gets obtained as the convex hull of the vertex set of half of 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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