Acronym trim (older: cacam, even older: tram, oldest: mak)
Name trirectified pentacontitetrapeton,
(centrocellated pentacontitetrapeton,
pentacontitetraheptacontidipeton)
Circumradius sqrt(2) = 1.414214

Incidence matrix according to Dynkin symbol

x3o3o3o3x *c3o

. . . . .    . | 270 |    8    8 |   24   32   24 |   32   48   48   32 |   8   32   8  24   32   8   8 |  8  1   8   8  1
---------------+-----+-----------+----------------+---------------------+-------------------------------+-----------------
x . . . .    . |   2 | 1080    * |    6    4    0 |   12   12    6    0 |   4   12   4   6    4   0   0 |  4  1   4   1  0
. . . . x    . |   2 |    * 1080 |    0    4    6 |    0    6   12   12 |   0    4   0   6   12   4   4 |  4  0   1   4  1
---------------+-----+-----------+----------------+---------------------+-------------------------------+-----------------
x3o . . .    . |   3 |    3    0 | 2160    *    * |    4    2    0    0 |   2    4   2   1    0   0   0 |  2  1   2   0  0
x . . . x    . |   4 |    2    2 |    * 2160    * |    0    3    3    0 |   0    3   0   3    3   0   0 |  3  0   1   1  0
. . . o3x    . |   3 |    0    3 |    *    * 2160 |    0    0    2    4 |   0    0   0   1    4   2   2 |  2  0   0   2  1
---------------+-----+-----------+----------------+---------------------+-------------------------------+-----------------
x3o3o . .    .    4 |    6    0 |    4    0    0 | 2160    *    *    * |   1    1   1   0    0   0   0 |  1  1   1   0  0
x3o . . x    .    6 |    6    3 |    2    3    0 |    * 2160    *    * |   0    2   0   1    0   0   0 |  2  0   1   0  0
x . . o3x    .    6 |    3    6 |    0    3    2 |    *    * 2160    * |   0    0   0   1    2   0   0 |  2  0   0   1  0
. . o3o3x    .    4 |    0    6 |    0    0    4 |    *    *    * 2160 |   0    0   0   0    1   1   1 |  1  0   0   1  1
---------------+-----+-----------+----------------+---------------------+-------------------------------+-----------------
x3o3o3o .    .    5 |   10    0 |   10    0    0 |    5    0    0    0 | 432    *   *   *    *   *   * |  1  1   0   0  0
x3o3o . x    .    8 |   12    4 |    8    6    0 |    2    4    0    0 |   * 1080   *   *    *   *   * |  1  0   1   0  0
x3o3o . . *c3o    5 |   10    0 |   10    0    0 |    5    0    0    0 |   *    * 432   *    *   *   * |  0  1   1   0  0
x3o . o3x    .    9 |    9    9 |    3    9    3 |    0    3    3    0 |   *    *   * 720    *   *   * |  2  0   0   0  0
x . o3o3x    .    8 |    4   12 |    0    6    8 |    0    0    4    2 |   *    *   *   * 1080   *   * |  1  0   0   1  0
. o3o3o3x    .    5 |    0   10 |    0    0   10 |    0    0    0    5 |   *    *   *   *    * 432   * |  1  0   0   0  1
. . o3o3x *c3o    5 |    0   10 |    0    0   10 |    0    0    0    5 |   *    *   *   *    *   * 432 |  0  0   0   1  1
---------------+-----+-----------+----------------+---------------------+-------------------------------+-----------------
x3o3o3o3x    .   30 |   60   60 |   60   90   60 |   30   60   60   30 |   6   15   0  20   15   6   0 | 72  *   *   *  *
x3o3o3o . *c3o   10 |   40    0 |   80    0    0 |   80    0    0    0 |  16    0  16   0    0   0   0 |  * 27   *   *  *
x3o3o . x *c3o   10 |   20    5 |   20   10    0 |   10   10    0    0 |   0    5   2   0    0   0   0 |  *  * 216   *  *
x . o3o3x *c3o   10 |    5   20 |    0   10   20 |    0    0   10   10 |   0    0   0   0    5   0   2 |  *  *   * 216  *
. o3o3o3x *c3o   10 |    0   40 |    0    0   80 |    0    0    0   80 |   0    0   0   0    0  16  16 |  *  *   *   * 27
or
. . . . .    .    | 270 |   16 |   48   32 |   64   96 |  16   64  16  24 |  8  2  16
------------------+-----+------+-----------+-----------+------------------+----------
x . . . .    .  & |   2 | 2160 |    6    4 |   12   18 |   4   16   4   6 |  4  1   5
------------------+-----+------+-----------+-----------+------------------+----------
x3o . . .    .  & |   3 |    3 | 4320    * |    4    2 |   2    4   2   1 |  2  1   2
x . . . x    .    |   4 |    4 |    * 2160 |    0    6 |   0    6   0   3 |  3  0   2
------------------+-----+------+-----------+-----------+------------------+----------
x3o3o . .    .  &    4 |    6 |    4    0 | 4320    * |   1    1   1   0 |  1  1   1
x3o . . x    .  &    6 |    9 |    2    3 |    * 4320 |   0    2   0   1 |  2  0   1
------------------+-----+------+-----------+-----------+------------------+----------
x3o3o3o .    .  &    5 |   10 |   10    0 |    5    0 | 864    *   *   * |  1  1   0
x3o3o . x    .  &    8 |   16 |    8    6 |    2    4 |   * 2160   *   * |  1  0   1
x3o3o . . *c3o  &    5 |   10 |   10    0 |    5    0 |   *    * 864   * |  0  1   1
x3o . o3x    .       9 |   18 |    6    9 |    0    6 |   *    *   * 720 |  2  0   0
------------------+-----+------+-----------+-----------+------------------+----------
x3o3o3o3x    .      30 |  120 |  120   90 |   60  120 |  12   30   0  20 | 72  *   *
x3o3o3o . *c3o  &   10 |   40 |   80    0 |   80    0 |  16    0  16   0 |  * 54   *
x3o3o . x *c3o  &   10 |   25 |   20   10 |   10   10 |   0    5   2   0 |  *  * 432

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