Acronym ...
Name dual of great antiprism
Circumradius ...
Vertex figure tet, p2p5p
Lace city
in approx. ASCII-art
                                          o5o                                   o5o                                          
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                      o5F           o5F                                                      
                                                                                                                             
                                          F5o                                   F5o                                          
           o5o                                   f5f                     f5f                                   o5o           
                                                                                                                             
                                                             F5x                                                             
                              F5o                                                           F5o                              
                                                                                                                             
                                          x5F                                   x5F                                          
                                                                                                                             
                              f5f                                                           f5f                              
                       o5F                                                                         o5F                       
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                              F5x                                                           F5x                              
                                                                                                                             
                  o5F                                                                                   o5F                  
                                                                                                                             
                                                                                                                             
o5o                    f5f                                   F5F                                   f5f                    o5o
                                                                                                                             
                                                                                                                             
                  F5o                                                                                   F5o                  
                                                                                                                             
                              x5F                                                           x5F                              
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                       F5o                                                                         F5o                       
                              f5f                                                           f5f                              
                                                                                                                             
                                          F5x                                   F5x                                          
                                                                                                                             
                              o5F                                                           o5F                              
                                                             x5F                                                             
                                                                                                                             
           o5o                                   f5f                     f5f                                   o5o           
                                          o5F                                   o5F                                          
                                                                                                                             
                                                      F5o           F5o                                                      
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                                                                                                             
                                          o5o                                   o5o                                          
Dihedral angles
  • at long edges:   144°
  • at short edges:   144°
Dual gap
Confer
uniform relative:
hi  

The cells can also be obtained as a stellation of doe by blending at 2 neighbouring pentagons with tall pyramids, which are the tips of sissid and then inserting inbetween a wedge type simplex, as is used for gad.

The faces are regular pentagons of side v = (sqrt(5)-1)/2 = 0.618034; kites {(k,K,K,K)} with corner angle k = 36° and K = 108°, where side KK has size v again, diagonal KK has size x = 1, side kK has size f = (1+sqrt(5))/2 = 1.618034, and the diagonal kK has size sqrt[(5+sqrt(5))/2] = 1.902113; and trapzia {(t,t,T,T)} with corner angle t = 72° and T = 108°, where the side TT has size v again, while the other sides tT and tt have both size f again.


Incidence matrix according to Dynkin symbol


of|foxfv-5-of|ofxvf-2-fo|fvxof-5-fo|vfxfo-&#z(f,v)   → existing heights = 0,
                                                       lacing(1,3) = lacing(1,4) = lacing(2,6) = lacing(2,7) = f
                                                       lacing(3,5) = lacing(4,5) = lacing(5,6) = lacing(6,7) = v

o. ..... 5 o. ..... 2 o. ..... 5 o. .....         | 10  *  *  *   *  *  *  1 1  5  5 0 0  0  0  0   0  0   0   0   0  0  0 |  5  5  10  0  0   0  0  0  0  0 |  5  5  0  0
.o ..... 5 .o ..... 2 .o ..... 5 .o .....         |  * 10  *  *   *  *  *  0 0  0  0 1 1  5  5  0   0  0   0   0   0  0  0 |  0  0   0  5  5  10  0  0  0  0 |  0  0  5  5
.. o.... 5 .. o.... 2 .. o.... 5 .. o....         |  *  * 50  *   *  *  *  0 0  1  0 0 0  0  0  1   2  0   0   0   0  0  0 |  1  0   2  0  0   0  2  1  0  0 |  1  2  1  0
.. .o... 5 .. .o... 2 .. .o... 5 .. .o...         |  *  *  * 50   *  *  *  0 0  0  1 0 0  0  0  0   0  1   2   0   0  0  0 |  0  1   2  0  0   0  0  0  2  1 |  2  1  0  1
.. ..o.. 5 .. ..o.. 2 .. ..o.. 5 .. ..o..         |  *  *  *  * 100  *  *  0 0  0  0 0 0  0  0  0   1  0   1   1   1  0  0 |  0  0   1  0  0   1  1  1  1  1 |  1  1  1  1
.. ...o. 5 .. ...o. 2 .. ...o. 5 .. ...o.         |  *  *  *  *   * 50  *  0 0  0  0 0 0  1  0  0   0  0   0   2   0  1  0 |  0  0   0  1  0   2  0  2  1  0 |  1  0  2  1
.. ....o 5 .. ....o 2 .. ....o 5 .. ....o         |  *  *  *  *   *  * 50  0 0  0  0 0 0  0  1  0   0  0   0   0   2  0  1 |  0  0   0  0  1   2  1  0  0  2 |  0  1  1  2
--------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------
.. .....   .. .....   f. .....   .. .....         |  2  0  0  0   0  0  0 | 5 *  *  * * *  *  *  *   *  *   *   *   *  *  * |  0  5   0  0  0   0  0  0  0  0 |  5  0  0  0  f
.. .....   .. .....   .. .....   f. .....         |  2  0  0  0   0  0  0 | * 5  *  * * *  *  *  *   *  *   *   *   *  *  * |  5  0   0  0  0   0  0  0  0  0 |  0  5  0  0  f
o. o.... 5 o. o.... 2 o. o.... 5 o. o....&#f      |  1  0  1  0   0  0  0 | * * 50  * * *  *  *  *   *  *   *   *   *  *  * |  1  0   2  0  0   0  0  0  0  0 |  1  2  0  0  f
o. .o... 5 o. .o... 2 o. .o... 5 o. .o...&#f      |  1  0  0  1   0  0  0 | * *  * 50 * *  *  *  *   *  *   *   *   *  *  * |  0  1   2  0  0   0  0  0  0  0 |  2  1  0  0  f
.f .....   .. .....   .. .....   .. .....         |  0  2  0  0   0  0  0 | * *  *  * 5 *  *  *  *   *  *   *   *   *  *  * |  0  0   0  0  5   0  0  0  0  0 |  0  0  0  5  f
.. .....   .f .....   .. .....   .. .....         |  0  2  0  0   0  0  0 | * *  *  * * 5  *  *  *   *  *   *   *   *  *  * |  0  0   0  5  0   0  0  0  0  0 |  0  0  5  0  f
.o ...o. 5 .o ...o. 2 .o ...o. 5 .o ...o.&#f      |  0  1  0  0   0  1  0 | * *  *  * * * 50  *  *   *  *   *   *   *  *  * |  0  0   0  1  0   2  0  0  0  0 |  0  0  2  1  f
.o ....o 5 .o ....o 2 .o ....o 5 .o ....o&#f      |  0  1  0  0   0  0  1 | * *  *  * * *  * 50  *   *  *   *   *   *  *  * |  0  0   0  0  1   2  0  0  0  0 |  0  0  1  2  f
.. .....   .. .....   .. .....   .. v....         |  0  0  2  0   0  0  0 | * *  *  * * *  *  * 25   *  *   *   *   *  *  * |  1  0   0  0  0   0  2  0  0  0 |  0  2  1  0  v
.. o.o.. 5 .. o.o.. 2 .. o.o.. 5 .. o.o..&#v      |  0  0  1  0   1  0  0 | * *  *  * * *  *  *  * 100  *   *   *   *  *  * |  0  0   1  0  0   0  1  1  0  0 |  1  1  1  0  v
.. .....   .. .....   .. .v...   .. .....         |  0  0  0  2   0  0  0 | * *  *  * * *  *  *  *   * 25   *   *   *  *  * |  0  1   0  0  0   0  0  0  2  0 |  2  0  0  1  v
.. .oo.. 5 .. .oo.. 2 .. .oo.. 5 .. .oo..&#v      |  0  0  0  1   1  0  0 | * *  *  * * *  *  *  *   *  * 100   *   *  *  * |  0  0   1  0  0   0  0  0  1  1 |  1  1  0  1  v
.. ..oo. 5 .. ..oo. 2 .. ..oo. 5 .. ..oo.&#v      |  0  0  0  0   1  1  0 | * *  *  * * *  *  *  *   *  *   * 100   *  *  * |  0  0   0  0  0   1  0  1  1  0 |  1  0  1  1  v
.. ..o.o 5 .. ..o.o 2 .. ..o.o 5 .. ..o.o&#v      |  0  0  0  0   1  0  1 | * *  *  * * *  *  *  *   *  *   *   * 100  *  * |  0  0   0  0  0   1  1  0  0  1 |  0  1  1  1  v
.. .....   .. ...v.   .. .....   .. .....         |  0  0  0  0   0  2  0 | * *  *  * * *  *  *  *   *  *   *   *   * 25  * |  0  0   0  1  0   0  0  2  0  0 |  1  0  2  0  v
.. ....v   .. .....   .. .....   .. .....         |  0  0  0  0   0  0  2 | * *  *  * * *  *  *  *   *  *   *   *   *  * 25 |  0  0   0  0  1   0  0  0  0  2 |  0  1  0  2  v
--------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------
.. .....   .. .....   .. .....   f. v....&#f      |  2  0  2  0   0  0  0 | 0 1  2  0 0 0  0  0  1   0  0   0   0   0  0  0 | 25  *   *  *  *   *  *  *  *  * |  0  2  0  0  {(k,K,K,K)}
.. .....   .. .....   f. .v...   .. .....&#f      |  2  0  0  2   0  0  0 | 1 0  0  2 0 0  0  0  0   0  1   0   0   0  0  0 |  * 25   *  *  *   *  *  *  *  * |  2  0  0  0  {(k,K,K,K)}
o. ooo.. 5 o. ooo.. 2 o. ooo.. 5 o. ooo..&#r(f,v) |  1  0  1  1   1  0  0 | 0 0  1  1 0 0  0  0  0   1  0   1   0   0  0  0 |  *  * 100  *  *   *  *  *  *  * |  1  1  0  0  {(t,t,T,T)}, cycle: (acfe)
.. .....   .f ...v.   .. .....   .. .....&#f      |  0  2  0  0   0  2  0 | 0 0  0  0 0 1  2  0  0   0  0   0   0   0  1  0 |  *  *   * 25  *   *  *  *  *  * |  0  0  2  0  {(k,K,K,K)}
.f ....v   .. .....   .. .....   .. .....&#f      |  0  2  0  0   0  0  2 | 0 0  0  0 1 0  0  2  0   0  0   0   0   0  0  1 |  *  *   *  * 25   *  *  *  *  * |  0  0  0  2  {(k,K,K,K)}
.o ..ooo 5 .o ..ooo 2 .o ..ooo 5 .o ..ooo&#r(f,v) |  0  1  0  0   1  1  1 | 0 0  0  0 0 0  1  1  0   0  0   0   1   1  0  0 |  *  *   *  *  * 100  *  *  *  * |  0  0  1  1  {(t,t,T,T)}, cycle: (bfeg)
.. .....   .. .....   .. .....   .. v.x.o&#vt     |  0  0  2  0   2  0  1 | 0 0  0  0 0 0  0  0  1   2  0   0   0   2  0  0 |  *  *   *  *  *   * 50  *  *  * |  0  1  1  0  v-{5}
.. .....   .. o.xv.   .. .....   .. .....&#vt     |  0  0  1  0   2  2  0 | 0 0  0  0 0 0  0  0  0   2  0   0   2   0  1  0 |  *  *   *  *  *   *  * 50  *  * |  1  0  1  0  v-{5}
.. .....   .. .....   .. .vxo.   .. .....&#vt     |  0  0  0  2   2  1  0 | 0 0  0  0 0 0  0  0  0   0  1   2   2   0  0  0 |  *  *   *  *  *   *  *  * 50  * |  1  0  0  1  v-{5}
.. .ox.v   .. .....   .. .....   .. .....&#vt     |  0  0  0  1   2  0  2 | 0 0  0  0 0 0  0  0  0   0  0   2   0   2  0  1 |  *  *   *  *  *   *  *  *  * 50 |  0  1  0  1  v-{5}
--------------------------------------------------+-----------------------+-------------------------------------------------+---------------------------------+------------
.. .....   o. ofxv.   f. fvxo.   .. .....&#(f,v)t   2  0  2  4   4  2  0 | 1 0  2  4 0 0  0  0  0   4  2   4   4   0  1  0 |  0  2   4  0  0   0  0  2  2  0 | 25  *  *  *  tower: a-d-c-e-f
o. fox.v   .. .....   .. .....   f. vfx.o&#(f,v)t   2  0  4  2   4  0  2 | 0 1  4  2 0 0  0  0  2   4  0   4   0   4  0  1 |  2  0   4  0  0   0  2  0  0  2 |  * 25  *  *  tower: a-c-d-e-g
.. .....   .f o.xvf   .. .....   .o v.xfo&#(f,v)t   0  2  2  0   4  4  2 | 0 0  0  0 0 1  4  2  1   4  0   0   4   4  2  0 |  0  0   0  2  0   4  2  2  0  0 |  *  * 25  *  tower: b-f-g-e-c
.f .oxfv   .. .....   .o .vxof   .. .....&#(f,v)t   0  2  0  2   4  2  4 | 0 0  0  0 1 0  2  4  0   0  1   4   4   4  0  2 |  0  0   0  0  2   4  0  0  2  2 |  *  *  * 25  tower: b-g-f-e-d

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