Acronym ...
Name isomorph of birectified pentacontitetrapeton
Circumradius sqrt(2/3) = 0.816497
Face vector 2160, 12960, 19440, 10800, 2286, 126

As abstract polytope this Grünbaumian polytope is isomorphic to barm, thereby replacing the retrograde by prograde triangles, 2thah by co, resp. 2tho+24{4} by rit and pinnip+5 2thah by srip, resp. the sirhin isomorph by sirhin and the sibrid isomorph by sibrid.


Incidence matrix according to Dynkin symbol

o3x3/2o3x3o *c3o

. .   . . .    . | 2160 |    6    6 |    3    6   12    6    3 |    3    6   12    2    6    3    2 |   6   1   3   6   4   1 |  3  2  2
-----------------+------+-----------+--------------------------+------------------------------------+-------------------------+---------
. x   . . .    . |    2 | 6480    * |    1    2    2    0    0 |    2    2    4    1    1    0    0 |   4   1   1   2   2   0 |  2  2  1
. .   . x .    . |    2 |    * 6480 |    0    0    2    2    1 |    0    1    4    0    2    2    1 |   2   0   1   4   2   1 |  2  1  2
-----------------+------+-----------+--------------------------+------------------------------------+-------------------------+---------
o3x   . . .    . |    3 |    3    0 | 2160    *    *    *    * |    2    2    0    0    0    0    0 |   4   1   1   0   0   0 |  2  2  0
. x3/2o . .    . |    3 |    3    0 |    * 4320    *    *    * |    1    0    2    1    0    0    0 |   2   1   0   1   2   0 |  1  2  1
. x   . x .    . |    4 |    2    2 |    *    * 6480    *    * |    0    1    2    0    1    0    0 |   2   0   1   2   1   0 |  2  1  1
. .   o3x .    . |    3 |    0    3 |    *    *    * 4320    * |    0    0    2    0    0    1    1 |   1   0   0   2   2   1 |  1  1  2
. .   . x3o    . |    3 |    0    3 |    *    *    *    * 2160 |    0    0    0    0    2    2    0 |   0   0   1   4   0   1 |  2  0  2
-----------------+------+-----------+--------------------------+------------------------------------+-------------------------+---------
o3x3/2o . .    .     6 |   12    0 |    4    4    0    0    0 | 1080    *    *    *    *    *    * |   2   1   0   0   0   0 |  1  2  0
o3x   . x .    .     6 |    6    3 |    2    0    3    0    0 |    * 2160    *    *    *    *    * |   2   0   1   0   0   0 |  2  1  0
. x3/2o3x .    .    12 |   12   12 |    0    4    6    4    0 |    *    * 2160    *    *    *    * |   1   0   0   1   1   0 |  1  1  1
. x3/2o . . *c3o     4 |    6    0 |    0    4    0    0    0 |    *    *    * 1080    *    *    * |   0   1   0   0   2   0 |  0  2  1
. x   . x3o    .     6 |    3    6 |    0    0    3    0    2 |    *    *    *    * 2160    *    * |   0   0   1   2   0   0 |  2  0  1
. .   o3x3o    .     6 |    0   12 |    0    0    0    4    4 |    *    *    *    *    * 1080    * |   0   0   0   2   0   1 |  1  0  2
. .   o3x . *c3o     4 |    0    6 |    0    0    0    4    0 |    *    *    *    *    *    * 1080 |   0   0   0   0   2   1 |  0  1  2
-----------------+------+-----------+--------------------------+------------------------------------+-------------------------+---------
o3x3/2o3x .    .    30 |   60   30 |   20   20   30   10    0 |    5   10    5    0    0    0    0 | 432   *   *   *   *   * |  1  1  0
o3x3/2o . . *c3o    10 |   30    0 |   10   20    0    0    0 |    5    0    0    5    0    0    0 |   * 216   *   *   *   * |  0  2  0
o3x   . x3o    .     9 |    9    9 |    3    0    9    0    3 |    0    3    0    0    3    0    0 |   *   * 720   *   *   * |  2  0  0
. x3/2o3x3o    .    30 |   30   60 |    0   10   30   20   20 |    0    0    5    0   10    5    0 |   *   *   * 432   *   * |  1  0  1
. x3/2o3x . *c3o    32 |   48   48 |    0   32   24   32    0 |    0    0    8    8    0    0    8 |   *   *   *   * 270   * |  0  1  1
. .   o3x3o *c3o    10 |    0   30 |    0    0    0   20   10 |    0    0    0    0    0    5    5 |   *   *   *   *   * 216 |  0  0  2
-----------------+------+-----------+--------------------------+------------------------------------+-------------------------+---------
o3x3/2o3x3o    .    90 |  180  180 |   60   60  180   60   60 |   15   60   30    0   60   15    0 |   6   0  20   6   0   0 | 72  *  *
o3x3/2o3x . *c3o   160 |  480  240 |  160  320  240  160    0 |   80   80   80   80    0    0   40 |  16  16   0   0  10   0 |  * 27  *
. x3/2o3x3o *c3o   160 |  240  480 |    0  160  240  320  160 |    0    0   80   40   80   80   80 |   0   0   0  16  10  16 |  *  * 27

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