Acronym grog
Name great rhombihexacontatetrapeton,
cantitruncated hexacross
Circumradius sqrt(7) = 2.645751
Coordinates (3/sqrt(2), sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3x3x3o3o4o

. . . . . . | 960 |   1   1    6 |   1    6   6   12 |   6   12  12    8 |  12   8   8   1 |  8  1  1
------------+-----+--------------+-------------------+-------------------+-----------------+---------
x . . . . . |   2 | 480   *    * |   1    6   0    0 |   6   12   0    0 |  12   8   0   0 |  8  1  0
. x . . . . |   2 |   * 480    * |   1    0   6    0 |   6    0  12    0 |  12   0   8   0 |  8  0  1
. . x . . . |   2 |   *   * 2880 |   0    1   1    4 |   1    4   4    4 |   4   4   4   1 |  4  1  1
------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x . . . . |   6 |   3   3    0 | 160    *   *    *    6    0   0    0 |  12   0   0   0 |  8  0  0
x . x . . . |   4 |   2   0    2 |   * 1440   *    * |   1    4   0    0 |   4   4   0   0 |  4  1  0
. x3x . . . |   6 |   0   3    3 |   *    * 960    * |   1    0   4    0 |   4   0   4   0 |  4  0  1
. . x3o . . |   3 |   0   0    3 |   *    *   * 3840 |   0    1   1    2 |   1   2   2   1 |  2  1  1
------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x . . .   24 |  12  12   12 |   4    6   4    0 | 240    *   *    * |   4   0   0   0 |  4  0  0
x . x3o . .    6 |   3   0    6 |   0    3   0    2 |   * 1920   *    * |   1   2   0   0 |  2  1  0
. x3x3o . .   12 |   0   6   12 |   0    0   4    4 |   *    * 960    * |   1   0   2   0 |  2  0  1
. . x3o3o .    4 |   0   0    6 |   0    0   0    4 |   *    *   * 1920 |   0   1   1   1 |  1  1  1
------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x3o . .   60 |  30  30   60 |  10   30  20   20 |   5   10   5    0 | 192   *   *   * |  2  0  0
x . x3o3o .    8 |   4   0   12 |   0    6   0    8 |   0    4   0    2 |   * 960   *   * |  1  1  0
. x3x3o3o .   20 |   0  10   30 |   0    0  10   20 |   0    0   5    5 |   *   * 384   * |  1  0  1
. . x3o3o4o    8 |   0   0   24 |   0    0   0   32 |   0    0   0   16 |   *   *   * 120 |  0  1  1
------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x3o3o .  120 |  60  60  180 |  20   90  60  120 |  15   60  30   30 |   6  15   6   0 | 64  *  *
x . x3o3o4o   16 |   8   0   48 |   0   24   0   64 |   0   32   0   32 |   0  16   0   2 |  * 60  *
. x3x3o3o4o   80 |   0  40  240 |   0    0  80  320 |   0    0  80  160 |   0   0  32  10 |  *  * 12

x3x3x3o3o4/3o

. . . . .   . | 960 |   1   1    6 |   1    6   6   12 |   6   12  12    8 |  12   8   8   1 |  8  1  1
--------------+-----+--------------+-------------------+-------------------+-----------------+---------
x . . . .   . |   2 | 480   *    * |   1    6   0    0 |   6   12   0    0 |  12   8   0   0 |  8  1  0
. x . . .   . |   2 |   * 480    * |   1    0   6    0 |   6    0  12    0 |  12   0   8   0 |  8  0  1
. . x . .   . |   2 |   *   * 2880 |   0    1   1    4 |   1    4   4    4 |   4   4   4   1 |  4  1  1
--------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x . . .   . |   6 |   3   3    0 | 160    *   *    *    6    0   0    0 |  12   0   0   0 |  8  0  0
x . x . .   . |   4 |   2   0    2 |   * 1440   *    * |   1    4   0    0 |   4   4   0   0 |  4  1  0
. x3x . .   . |   6 |   0   3    3 |   *    * 960    * |   1    0   4    0 |   4   0   4   0 |  4  0  1
. . x3o .   . |   3 |   0   0    3 |   *    *   * 3840 |   0    1   1    2 |   1   2   2   1 |  2  1  1
--------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x . .   .   24 |  12  12   12 |   4    6   4    0 | 240    *   *    * |   4   0   0   0 |  4  0  0
x . x3o .   .    6 |   3   0    6 |   0    3   0    2 |   * 1920   *    * |   1   2   0   0 |  2  1  0
. x3x3o .   .   12 |   0   6   12 |   0    0   4    4 |   *    * 960    * |   1   0   2   0 |  2  0  1
. . x3o3o   .    4 |   0   0    6 |   0    0   0    4 |   *    *   * 1920 |   0   1   1   1 |  1  1  1
--------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x3o .   .   60 |  30  30   60 |  10   30  20   20 |   5   10   5    0 | 192   *   *   * |  2  0  0
x . x3o3o   .    8 |   4   0   12 |   0    6   0    8 |   0    4   0    2 |   * 960   *   * |  1  1  0
. x3x3o3o   .   20 |   0  10   30 |   0    0  10   20 |   0    0   5    5 |   *   * 384   * |  1  0  1
. . x3o3o4/3o    8 |   0   0   24 |   0    0   0   32 |   0    0   0   16 |   *   *   * 120 |  0  1  1
--------------+-----+--------------+-------------------+-------------------+-----------------+---------
x3x3x3o3o   .  120 |  60  60  180 |  20   90  60  120 |  15   60  30   30 |   6  15   6   0 | 64  *  *
x . x3o3o4/3o   16 |   8   0   48 |   0   24   0   64 |   0   32   0   32 |   0  16   0   2 |  * 60  *
. x3x3o3o4/3o   80 |   0  40  240 |   0    0  80  320 |   0    0  80  160 |   0   0  32  10 |  *  * 12

o3o3o *b3x3x3x

. . .    . . . | 960 |    6   1   1 |   12   6    6   1 |   4   4  12   12   6 |   1   4   4   4   4  12 |  1  1  4  4
---------------+-----+--------------+-------------------+----------------------+-------------------------+------------
. . .    x . . |   2 | 2880   *   * |    4   1    1   0 |   2   2   4    4   1 |   1   2   2   2   2   4 |  1  1  2  2
. . .    . x . |   2 |    * 480   * |    0   6    0   1 |   0   0  12    0   6 |   0   4   0   4   0  12 |  1  0  4  4
. . .    . . x |   2 |    *   * 480 |    0   0    6   1 |   0   0   0   12   6 |   0   0   4   0   4  12 |  0  1  4  4
---------------+-----+--------------+-------------------+----------------------+-------------------------+------------
. o . *b3x . . |   3 |    3   0   0 | 3840   *    *   * |   1   1   1    1   0 |   1   1   1   1   1   1 |  1  1  1  1
. . .    x3x . |   6 |    3   3   0 |    * 960    *   * |   0   0   4    0   1 |   0   2   0   2   0   4 |  1  0  2  2
. . .    x . x |   4 |    2   0   2 |    *   * 1440   * |   0   0   0    4   1 |   0   0   2   0   2   4 |  0  1  2  2
. . .    . x3x |   6 |    0   3   3 |    *   *    * 160    0   0   0    0   6 |   0   0   0   0   0  12 |  0  0  4  4
---------------+-----+--------------+-------------------+----------------------+-------------------------+------------
o3o . *b3x . .    4 |    6   0   0 |    4   0    0   0 | 960   *   *    *   * |   1   1   1   0   0   0 |  1  1  1  0
. o3o *b3x . .    4 |    6   0   0 |    4   0    0   0 |   * 960   *    *   * |   1   0   0   1   1   0 |  1  1  0  1
. o . *b3x3x .   12 |   12   6   0 |    4   4    0   0 |   *   * 960    *   * |   0   1   0   1   0   1 |  1  0  1  1
. o . *b3x . x    6 |    6   0   3 |    2   0    3   0 |   *   *   * 1920   * |   0   0   1   0   1   1 |  0  1  1  1
. . .    x3x3x   24 |   12  12  12 |    0   4    6   4 |   *   *   *    * 240 |   0   0   0   0   0   4 |  0  0  2  2
---------------+-----+--------------+-------------------+----------------------+-------------------------+------------
o3o3o *b3x . .    8 |   24   0   0 |   32   0    0   0 |   8   8   0    0   0 | 120   *   *   *   *   * |  1  1  0  0
o3o . *b3x3x .   20 |   30  10   0 |   20  10    0   0 |   5   0   5    0   0 |   * 192   *   *   *   * |  1  0  1  0
o3o . *b3x . x    8 |   12   0   4 |    8   0    6   0 |   2   0   0    4   0 |   *   * 480   *   *   * |  0  1  1  0
. o3o *b3x3x .   20 |   30  10   0 |   20  10    0   0 |   0   5   5    0   0 |   *   *   * 192   *   * |  1  0  0  1
. o3o *b3x . x    8 |   12   0   4 |    8   0    6   0 |   0   2   0    4   0 |   *   *   *   * 480   * |  0  1  0  1
. o . *b3x3x3x   60 |   60  30  30 |   20  20   30  10 |   0   0   5   10   5 |   *   *   *   *   * 192 |  0  0  1  1
---------------+-----+--------------+-------------------+----------------------+-------------------------+------------
o3o3o *b3x3x .   80 |  240  40   0 |  320  80    0   0 |  80  80  80    0   0 |  10  16   0  16   0   0 | 12  *  *  *
o3o3o *b3x . x   16 |   48   0   8 |   64   0   24   0 |  16  16   0   32   0 |   2   0   8   0   8   0 |  * 60  *  *
o3o . *b3x3x3x  120 |  180  60  60 |  120  60   90  20 |  30   0  30   60  15 |   0   6  15   0   0   6 |  *  * 32  *
. o3o *b3x3x3x  120 |  180  60  60 |  120  60   90  20 |   0  30  30   60  15 |   0   0   0   6  15   6 |  *  *  * 32

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