Acronym ...
Name 2grahi (?)
Circumradius sqrt[64+28 sqrt(5)] = 11.252107
General of army grahi
Colonel of regiment grahi
Confer
non-Grünbaumian master:
grahi  

Looks like a compound of 2 great rhombated hecatonicosachora (grahi), and indeed all but the Grünbaumian elements coincide by pairs.


Incidence matrix according to Dynkin symbol

β3x3x5x

both( . . . . ) | 14400 |    1    1    1    1 |    1    1    1    1    1    1 |   1   1    1   1
----------------+-------+---------------------+-------------------------------+-----------------
both( . x . . ) |     2 | 7200    *    *    * |    1    1    0    1    0    0 |   1   1    1   0
both( . . x . ) |     2 |    * 7200    *    * |    1    0    1    0    1    0 |   1   1    0   1
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( . x3x . ) |     6 |    3    3    0    0 | 2400    *    *    *    *    * |   1   1    0   0
both( . x . x ) |     4 |    2    0    2    0 |    * 3600    *    *    *    * |   1   0    1   0
both( . . x5x ) |    10 |    0    5    5    0 |    *    * 1440    *    *    * |   1   0    0   1
      β3x . .        6 |    3    0    0    3 |    *    *    * 2400    *    * |   0   1    1   0
sefa( β3x3x . ) |     6 |    0    3    0    3 |    *    *    *    * 2400    * |   0   1    0   1
sefa( β3x 2 x ) |     4 |    0    0    2    2 |    *    *    *    *    * 3600 |   0   0    1   1
----------------+-------+---------------------+-------------------------------+-----------------
both( . x3x5x )    120 |   60   60   60    0 |   20   30   12    0    0    0 | 120   *    *   *
      β3x3x .       24 |   12   12    0   12 |    4    0    0    4    4    0 |   * 600    *   *
      β3x 2 x       12 |    6    0    6    6 |    0    3    0    2    0    3 |   *   * 1200   *
sefa( β3x3x5x )    120 |    0   60   60   60 |    0    0   12    0   20   30 |   *   *    * 120

starting figure: x3x3x5x

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