Acronym prog
Name prismatorhombated hexacontatetrapeton,
runcicantellated hexacross
Circumradius 3
Coordinates (3/sqrt(2), sqrt(2), sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3o3x3x3o4o

. . . . . . | 2880 |    2    2    4 |   1    2    8   1    8    4 |   1    4    8    8   4    8   1 |   4    4   8   2   4   2 |  4   1  2  1
------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x . . . . . |    2 | 2880    *    * |   1    1    4   0    0    0 |   1    4    4    4   0    0   0 |   4    4   4   1   0   0 |  4   1  1  0
. . x . . . |    2 |    * 2880    * |   0    1    0   1    4    0 |   1    0    4    0   4    4   0 |   4    0   4   0   4   1 |  4   0  1  1
. . . x . . |    2 |    *    * 5760 |   0    0    2   0    2    2 |   0    1    2    4   1    4   1 |   1    2   4   2   2   2 |  2   1  2  1
------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o . . . . |    3 |    3    0    0 | 960    *    *   *    *    * |   1    4    0    0   0    0   0 |   4    4   0   0   0   0 |  4   1  0  0
x . x . . . |    4 |    2    2    0 |   * 1440    *   *    *    * |   1    0    4    0   0    0   0 |   4    0   4   0   0   0 |  4   0  1  0
x . . x . . |    4 |    2    0    2 |   *    * 5760   *    *    * |   0    1    1    2   0    0   0 |   1    2   2   1   0   0 |  2   1  1  0
. o3x . . . |    3 |    0    3    0 |   *    *    * 960    *    * |   1    0    0    0   4    0   0 |   4    0   0   0   4   0 |  4   0  0  1
. . x3x . . |    6 |    0    3    3 |   *    *    *   * 3840    * |   0    0    1    0   1    2   0 |   1    0   2   0   2   1 |  2   0  1  1
. . . x3o . |    3 |    0    0    3 |   *    *    *   *    * 3840 |   0    0    0    2   0    2   1 |   0    1   2   2   1   2 |  1   1  2  1
------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x . . .    12 |   12   12    0 |   4    6    0   4    0    0 | 240    *    *    *   *    *   * |   4    0   0   0   0   0 |  4   0  0  0
x3o . x . .     6 |    6    0    3 |   2    0    3   0    0    0 |   * 1920    *    *   *    *   * |   1    2   0   0   0   0 |  2   1  0  0
x . x3x . .    12 |    6    6    6 |   0    3    3   0    2    0 |   *    * 1920    *   *    *   * |   1    0   2   0   0   0 |  2   0  1  0
x . . x3o .     6 |    3    0    6 |   0    0    3   0    0    2 |   *    *    * 3840   *    *   * |   0    1   1   1   0   0 |  1   1  1  0
. o3x3x . .    12 |    0   12    6 |   0    0    0   4    4    0 |   *    *    *    * 960    *   * |   1    0   0   0   2   0 |  2   0  0  1
. . x3x3o .    12 |    0    6   12 |   0    0    0   0    4    4 |   *    *    *    *   * 1920   * |   0    0   1   0   1   1 |  1   0  1  1
. . . x3o4o     6 |    0    0   12 |   0    0    0   0    0    8 |   *    *    *    *   *    * 480 |   0    0   0   2   0   2 |  0   1  2  1
------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x3x . .    60 |   60   60   30 |  20   30   30  20   20    0 |   5   10   10    0   5    0   0 | 192    *   *   *   *   * |  2   0  0  0
x3o . x3o .     9 |    9    0    9 |   3    0    9   0    0    3 |   0    3    0    3   0    0   0 |   * 1280   *   *   *   * |  1   1  0  0
x . x3x3o .    24 |   12   12   24 |   0    6   12   0    8    8 |   0    0    4    4   0    2   0 |   *    * 960   *   *   * |  1   0  1  0
x . . x3o4o    12 |    6    0   24 |   0    0   12   0    0   16 |   0    0    0    8   0    0   2 |   *    *   * 480   *   * |  0   1  1  0
. o3x3x3o .    30 |    0   30   30 |   0    0    0  10   20   10 |   0    0    0    0   5    5   0 |   *    *   *   * 384   * |  1   0  0  1
. . x3x3o4o    48 |    0   24   96 |   0    0    0   0   32   64 |   0    0    0    0   0   16   8 |   *    *   *   *   * 120 |  0   0  1  1
------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x3x3o .   180 |  180  180  180 |  60   90  180  60  120   60 |  15   60   60   60  30   30   0 |   6   20  15   0   6   0 | 64   *  *  *
x3o . x3o4o    18 |   18    0   36 |   6    0   36   0    0   24 |   0   12    0   24   0    0   3 |   0    8   0   3   0   0 |  * 160  *  *
x . x3x3o4o    96 |   48   48  192 |   0   24   96   0   64  128 |   0    0   32   64   0   32  16 |   0    0  16   8   0   2 |  *   * 60  *
. o3x3x3o4o   240 |    0  240  480 |   0    0    0  80  320  320 |   0    0    0    0  80  160  40 |   0    0   0   0  32  10 |  *   *  * 12

x3o3x3x3o4/3o

. . . . .   . | 2880 |    2    2    4 |   1    2    8   1    8    4 |   1    4    8    8   4    8   1 |   4    4   8   2   4   2 |  4   1  2  1
--------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x . . . .   . |    2 | 2880    *    * |   1    1    4   0    0    0 |   1    4    4    4   0    0   0 |   4    4   4   1   0   0 |  4   1  1  0
. . x . .   . |    2 |    * 2880    * |   0    1    0   1    4    0 |   1    0    4    0   4    4   0 |   4    0   4   0   4   1 |  4   0  1  1
. . . x .   . |    2 |    *    * 5760 |   0    0    2   0    2    2 |   0    1    2    4   1    4   1 |   1    2   4   2   2   2 |  2   1  2  1
--------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o . . .   . |    3 |    3    0    0 | 960    *    *   *    *    * |   1    4    0    0   0    0   0 |   4    4   0   0   0   0 |  4   1  0  0
x . x . .   . |    4 |    2    2    0 |   * 1440    *   *    *    * |   1    0    4    0   0    0   0 |   4    0   4   0   0   0 |  4   0  1  0
x . . x .   . |    4 |    2    0    2 |   *    * 5760   *    *    * |   0    1    1    2   0    0   0 |   1    2   2   1   0   0 |  2   1  1  0
. o3x . .   . |    3 |    0    3    0 |   *    *    * 960    *    * |   1    0    0    0   4    0   0 |   4    0   0   0   4   0 |  4   0  0  1
. . x3x .   . |    6 |    0    3    3 |   *    *    *   * 3840    * |   0    0    1    0   1    2   0 |   1    0   2   0   2   1 |  2   0  1  1
. . . x3o   . |    3 |    0    0    3 |   *    *    *   *    * 3840 |   0    0    0    2   0    2   1 |   0    1   2   2   1   2 |  1   1  2  1
--------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x . .   .    12 |   12   12    0 |   4    6    0   4    0    0 | 240    *    *    *   *    *   * |   4    0   0   0   0   0 |  4   0  0  0
x3o . x .   .     6 |    6    0    3 |   2    0    3   0    0    0 |   * 1920    *    *   *    *   * |   1    2   0   0   0   0 |  2   1  0  0
x . x3x .   .    12 |    6    6    6 |   0    3    3   0    2    0 |   *    * 1920    *   *    *   * |   1    0   2   0   0   0 |  2   0  1  0
x . . x3o   .     6 |    3    0    6 |   0    0    3   0    0    2 |   *    *    * 3840   *    *   * |   0    1   1   1   0   0 |  1   1  1  0
. o3x3x .   .    12 |    0   12    6 |   0    0    0   4    4    0 |   *    *    *    * 960    *   * |   1    0   0   0   2   0 |  2   0  0  1
. . x3x3o   .    12 |    0    6   12 |   0    0    0   0    4    4 |   *    *    *    *   * 1920   * |   0    0   1   0   1   1 |  1   0  1  1
. . . x3o4/3o     6 |    0    0   12 |   0    0    0   0    0    8 |   *    *    *    *   *    * 480 |   0    0   0   2   0   2 |  0   1  2  1
--------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x3x .   .    60 |   60   60   30 |  20   30   30  20   20    0 |   5   10   10    0   5    0   0 | 192    *   *   *   *   * |  2   0  0  0
x3o . x3o   .     9 |    9    0    9 |   3    0    9   0    0    3 |   0    3    0    3   0    0   0 |   * 1280   *   *   *   * |  1   1  0  0
x . x3x3o   .    24 |   12   12   24 |   0    6   12   0    8    8 |   0    0    4    4   0    2   0 |   *    * 960   *   *   * |  1   0  1  0
x . . x3o4/3o    12 |    6    0   24 |   0    0   12   0    0   16 |   0    0    0    8   0    0   2 |   *    *   * 480   *   * |  0   1  1  0
. o3x3x3o   .    30 |    0   30   30 |   0    0    0  10   20   10 |   0    0    0    0   5    5   0 |   *    *   *   * 384   * |  1   0  0  1
. . x3x3o4/3o    48 |    0   24   96 |   0    0    0   0   32   64 |   0    0    0    0   0   16   8 |   *    *   *   *   * 120 |  0   0  1  1
--------------+------+----------------+-----------------------------+---------------------------------+--------------------------+-------------
x3o3x3x3o   .   180 |  180  180  180 |  60   90  180  60  120   60 |  15   60   60   60  30   30   0 |   6   20  15   0   6   0 | 64   *  *  *
x3o . x3o4/3o    18 |   18    0   36 |   6    0   36   0    0   24 |   0   12    0   24   0    0   3 |   0    8   0   3   0   0 |  * 160  *  *
x . x3x3o4/3o    96 |   48   48  192 |   0   24   96   0   64  128 |   0    0   32   64   0   32  16 |   0    0  16   8   0   2 |  *   * 60  *
. o3x3x3o4/3o   240 |    0  240  480 |   0    0    0  80  320  320 |   0    0    0    0  80  160  40 |   0    0   0   0  32  10 |  *   *  * 12

o3x3o *b3x3o3x

. . .    . . . | 2880 |    4    2    2 |    2    2    8    8   1    2   1 |   1   4    4   4    4   4    8    4   1 |   2   2   2   4   2   2   4   2   4 |  1  2   1  2  2
---------------+------+----------------+----------------------------------+-----------------------------------------+-------------------------------------+----------------
. x .    . . . |    2 | 5760    *    * |    1    1    2    2   0    0   0 |   1   2    2   2    2   1    2    1   0 |   2   2   1   2   1   1   2   1   1 |  1  2   1  1  1
. . .    x . . |    2 |    * 2880    * |    0    0    4    0   1    1   0 |   0   2    0   2    0   4    4    0   1 |   1   0   2   2   0   2   2   0   4 |  1  1   0  2  2
. . .    . . x |    2 |    *    * 2880 |    0    0    0    4   0    1   1 |   0   0    2   0    2   0    4    4   1 |   0   1   0   2   2   0   2   2   4 |  0  1   1  2  2
---------------+------+----------------+----------------------------------+-----------------------------------------+-------------------------------------+----------------
o3x .    . . . |    3 |    3    0    0 | 1920    *    *    *   *    *   * |   1   2    2   0    0   0    0    0   0 |   2   2   1   2   1   0   0   0   0 |  1  2   1  1  0
. x3o    . . . |    3 |    3    0    0 |    * 1920    *    *   *    *   * |   1   0    0   2    2   0    0    0   0 |   2   2   0   0   0   1   2   1   0 |  1  2   1  0  1
. x . *b3x . . |    6 |    3    3    0 |    *    * 3840    *   *    *   * |   0   1    0   1    0   1    1    0   0 |   1   0   1   1   0   1   1   0   1 |  1  1   0  1  1
. x .    . . x |    4 |    2    0    2 |    *    *    * 5760   *    *   * |   0   0    1   0    1   0    1    1   0 |   0   1   0   1   1   0   1   1   1 |  0  1   1  1  1
. . .    x3o . |    3 |    0    3    0 |    *    *    *    * 960    *   * |   0   0    0   0    0   4    0    0   1 |   0   0   2   0   0   2   0   0   4 |  1  0   0  2  2
. . .    x . x |    4 |    0    2    2 |    *    *    *    *   * 1440   * |   0   0    0   0    0   0    4    0   1 |   0   0   0   2   0   0   2   0   4 |  0  1   0  2  2
. . .    . o3x |    3 |    0    0    3 |    *    *    *    *   *    * 960 |   0   0    0   0    0   0    0    4   1 |   0   0   0   0   2   0   0   2   4 |  0  0   1  2  2
---------------+------+----------------+----------------------------------+-----------------------------------------+-------------------------------------+----------------
o3x3o    . . .     6 |   12    0    0 |    4    4    0    0   0    0   0 | 480   *    *   *    *   *    *    *   * |   2   2   0   0   0   0   0   0   0 |  1  2   1  0  0
o3x . *b3x . .    12 |   12    6    0 |    4    0    4    0   0    0   0 |   * 960    *   *    *   *    *    *   * |   1   0   1   1   0   0   0   0   0 |  1  1   0  1  0
o3x .    . . x     6 |    6    0    3 |    2    0    0    3   0    0   0 |   *   * 1920   *    *   *    *    *   * |   0   1   0   1   1   0   0   0   0 |  0  1   1  1  0
. x3o *b3x . .    12 |   12    6    0 |    0    4    4    0   0    0   0 |   *   *    * 960    *   *    *    *   * |   1   0   0   0   0   1   1   0   0 |  1  1   0  0  1
. x3o    . . x     6 |    6    0    3 |    0    2    0    3   0    0   0 |   *   *    *   * 1920   *    *    *   * |   0   1   0   0   0   0   1   1   0 |  0  1   1  0  1
. x . *b3x3o .    12 |    6   12    0 |    0    0    4    0   4    0   0 |   *   *    *   *    * 960    *    *   * |   0   0   1   0   0   1   0   0   1 |  1  0   0  1  1
. x . *b3x . x    12 |    6    6    6 |    0    0    2    3   0    3   0 |   *   *    *   *    *   * 1920    *   * |   0   0   0   1   0   0   1   0   1 |  0  1   0  1  1
. x .    . o3x     6 |    3    0    6 |    0    0    0    3   0    0   2 |   *   *    *   *    *   *    * 1920   * |   0   0   0   0   1   0   0   1   1 |  0  0   1  1  1
. . .    x3o3x    12 |    0   12   12 |    0    0    0    0   4    6   4 |   *   *    *   *    *   *    *    * 240 |   0   0   0   0   0   0   0   0   4 |  0  0   0  2  2
---------------+------+----------------+----------------------------------+-----------------------------------------+-------------------------------------+----------------
o3x3o *b3x . .    48 |   96   24    0 |   32   32   32    0   0    0   0 |   8   8    0   8    0   0    0    0   0 | 120   *   *   *   *   *   *   *   * |  1  1   0  0  0
o3x3o    . . x    12 |   24    0    6 |    8    8    0   12   0    0   0 |   2   0    4   0    4   0    0    0   0 |   * 480   *   *   *   *   *   *   * |  0  1   1  0  0
o3x . *b3x3o .    30 |   30   30    0 |   10    0   20    0  10    0   0 |   0   5    0   0    0   5    0    0   0 |   *   * 192   *   *   *   *   *   * |  1  0   0  1  0
o3x . *b3x . x    24 |   24   12   12 |    8    0    8   12   0    6   0 |   0   2    4   0    0   0    4    0   0 |   *   *   * 480   *   *   *   *   * |  0  1   0  1  0
o3x .    . o3x     9 |    9    0    9 |    3    0    0    9   0    0   3 |   0   0    3   0    0   0    0    3   0 |   *   *   *   * 640   *   *   *   * |  0  0   1  1  0
. x3o *b3x3o .    30 |   30   30    0 |    0   10   20    0  10    0   0 |   0   0    0   5    0   5    0    0   0 |   *   *   *   *   * 192   *   *   * |  1  0   0  0  1
. x3o *b3x . x    24 |   24   12   12 |    0    8    8   12   0    6   0 |   0   0    0   2    4   0    4    0   0 |   *   *   *   *   *   * 480   *   * |  0  1   0  0  1
. x3o    . o3x     9 |    9    0    9 |    0    3    0    9   0    0   3 |   0   0    0   0    3   0    0    3   0 |   *   *   *   *   *   *   * 640   * |  0  0   1  0  1
. x . *b3x3o3x    60 |   30   60   60 |    0    0   20   30  20   30  20 |   0   0    0   0    0   5   10   10   5 |   *   *   *   *   *   *   *   * 192 |  0  0   0  1  1
---------------+------+----------------+----------------------------------+-----------------------------------------+-------------------------------------+----------------
o3x3o *b3x3o .   240 |  480  240    0 |  160  160  320    0  80    0   0 |  40  80    0  80    0  80    0    0   0 |  10   0  16   0   0  16   0   0   0 | 12  *   *  *  *
o3x3o *b3x . x    96 |  192   48   48 |   64   64   64   96   0   24   0 |  16  16   32  16   32   0   32    0   0 |   2   8   0   8   0   0   8   0   0 |  * 60   *  *  *
o3x3o    . o3x    18 |   36    0   18 |   12   12    0   36   0    0   6 |   3   0   12   0   12   0    0   12   0 |   0   3   0   0   4   0   0   4   0 |  *  * 160  *  *
o3x . *b3x3o3x   180 |  180  180  180 |   60    0  120  180  60   90  60 |   0  30   60   0    0  30   60   60  15 |   0   0   6  15  20   0   0   0   6 |  *  *   * 32  *
. x3o *b3x3o3x   180 |  180  180  180 |    0   60  120  180  60   90  60 |   0   0    0  30   60  30   60   60  15 |   0   0   0   0   0   6  15  20   6 |  *  *   *  * 32

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