Acronym ...
Name 2srahi (?)
Circumradius sqrt[23+10 sqrt(5)] = 6.735034
General of army srahi
Colonel of regiment srahi
Confer
non-Grünbaumian master:
srahi  
Grünbaumian relatives:
2srahi+1440{10}+4800{3}   2srahi+2400trip  

Looks like a compound of 2 coincident small rhombated hecatonicosachora (srahi), and indeed all but the Grünbaumian elements coincide by pairs. It comes in different types depending on which cells are Grünbaumian: type A uses all but the small rhombicosidodecahedra (srid) as Grünbaumian cells, while type B uses all but the triangular prisms (trip) as such. Type B even splits according to the used version of the Grünbaumian doubly covered small rhombicosidodecahedral cells (2srid (?)): in type B1 the small rhombicosidodecahedral pentagons will be replaced by {10/2}, in type B2 they remain as pairs of coincident {5}.


Incidence matrix according to Dynkin symbol

β3x3o5x   (type A)

both( . . . . ) | 7200 |    2    2    2 |    1    2    1    2    1    2 |   1   1    2   1
----------------+------+----------------+-------------------------------+-----------------
both( . x . . ) |    2 | 7200    *    * |    1    1    0    1    0    0 |   1   1    1   0
both( . . . x ) |    2 |    * 7200    * |    0    1    1    0    0    1 |   1   0    1   1
sefa( β3x . . ) |    2 |    *    * 7200 |    0    0    0    1    1    1 |   0   1    1   1
----------------+------+----------------+-------------------------------+-----------------
both( . x3o . ) |    3 |    3    0    0 | 2400    *    *    *    *    * |   1   1    0   0
both( . x . x ) |    4 |    2    2    0 |    * 3600    *    *    *    * |   1   0    1   0
both( . . o5x ) |    5 |    0    5    0 |    *    * 1440    *    *    * |   1   0    0   1
      β3x . .       6 |    3    0    3 |    *    *    * 2400    *    * |   0   1    1   0
sefa( β3x3o . ) |    3 |    0    0    3 |    *    *    *    * 2400    * |   0   1    0   1
sefa( β3x 2 x ) |    4 |    0    2    2 |    *    *    *    *    * 3600 |   0   0    1   1
----------------+------+----------------+-------------------------------+-----------------
both( . x3o5x )    60 |   60   60    0 |   20   30   12    0    0    0 | 120   *    *   *
      β3xo3 .      12 |   12    0   12 |    4    0    0    4    4    0 |   * 600    *   *
      β3x 2 x      12 |    6    6    6 |    0    3    0    2    0    3 |   *   * 1200   *
sefa( β3x3o5x )    60 |    0   60   60 |    0    0   12    0   20   30 |   *   *    * 120

starting figure: x3x3o5x

o3x3β5x   (type B1)

both( . . . . ) | 7200 |    2    1    2    1 |    1    2    2   1    1    2 |    1   1   2    1
----------------+------+---------------------+------------------------------+------------------
both( . x . . ) |    2 | 7200    *    *    * |    1    1    1   0    0    0 |    1   1   1    0
both( . . . x ) |    2 |    * 3600    *    * |    0    2    0   1    0    0 |    1   0   2    0
sefa( . x3β . ) |    2 |    *    * 7200    * |    0    0    1   0    1    1 |    0   1   1    1
sefa( . . β5x ) |    2 |    *    *    * 3600 |    0    0    0   1    0    2 |    0   0   2    1
----------------+------+---------------------+------------------------------+------------------
both( o3x . . ) |    3 |    3    0    0    0 | 2400    *    *   *    *    * |    1   1   0    0
both( . x . x ) |    4 |    2    2    0    0 |    * 3600    *   *    *    * |    1   0   1    0
      . x3β .       6 |    3    0    3    0 |    *    * 2400   *    *    * |    0   1   1    0
      . . β5x      10 |    0    5    0    5 |    *    *    * 720    *    * |    0   0   2    0
sefa( o3x3β . ) |    3 |    0    0    3    0 |    *    *    *   * 2400    * |    0   1   0    1
sefa( . x3β5x ) |    4 |    0    0    2    2 |    *    *    *   *    * 3600 |    0   0   1    1
----------------+------+---------------------+------------------------------+------------------
both( o3x . x )     6 |    6    3    0    0 |    2    3    0   0    0    0 | 1200   *   *    *
      o3x3β .      12 |   12    0   12    0 |    4    0    4   0    4    0 |    * 600   *    *
      . x3β5x     120 |   60   60   60   60 |    0   30   20  12    0   30 |    *   * 120    *
sefa( o3x3β5x )     6 |    0    0    6    3 |    0    0    0   0    2    3 |    *   *   * 1200

starting figure: o3x3x5x

o3x3β5β   (type B2)

both( . . . . ) | 7200 |    2    2    2 |    1    2    1    1    4 |   1   2    2
----------------+------+----------------+--------------------------+-------------
both( . x . . ) |    2 | 7200    *    * |    1    1    0    0    1 |   1   1    1
sefa( . x3β . ) |    2 |    * 7200    * |    0    1    0    1    1 |   1   1    1
sefa( . . s5s ) |    2 |    *    * 7200 |    0    0    1    0    2 |   0   2    1
----------------+------+----------------+--------------------------+-------------
both( o3x . . ) |    3 |    3    0    0 | 2400    *    *    *    * |   1   0    1
      . x3β .       6 |    3    3    0 |    * 2400    *    *    * |   1   1    0
both( . . s5s )     5 |    0    0    5 |    *    * 1440    *    * |   0   2    0
sefa( o3x3β . ) |    3 |    0    3    0 |    *    *    * 2400    * |   1   0    1
sefa( . x3β5β ) |    4 |    1    1    2 |    *    *    *    * 7200 |   0   1    1
----------------+------+----------------+--------------------------+-------------
      o3x3β .      12 |   12   12    0 |    4    4    0    4    0 | 600   *    *
      . x3β5β     120 |   60   60  120 |    0   20   24    0   60 |   * 120    *
sefa( o3x3β5β )     6 |    3    3    3 |    1    0    0    1    3 |   *   * 2400

starting figure: o3x3x5x

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