Acronym gaborg Name great birhombihexacontitetrapeton,bicantitruncated hexacross Circumradius sqrt(23/2) = 3.391165 Coordinates (3/sqrt(2), 3/sqrt(2), sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign Externallinks

Incidence matrix according to Dynkin symbol

```o3x3x3x3o4o

. . . . . . | 2880 |    2    1    4 |   1   2    8    4    4 |   1    4   8    8   4   1 |   4    4   8   2  1 |  4   1  2
------------+------+----------------+------------------------+---------------------------+---------------------+----------
. x . . . . |    2 | 2880    *    * |   1   1    4    0    0 |   1    4   4    4   0   0 |   4    4   4   1  0 |  4   1  1
. . x . . . |    2 |    * 1440    * |   0   2    0    4    0 |   1    0   8    0   4   0 |   4    0   8   0  1 |  4   0  2
. . . x . . |    2 |    *    * 5760 |   0   0    2    1    2 |   0    1   2    4   2   1 |   1    2   4   2  1 |  2   1  2
------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x . . . . |    3 |    3    0    0 | 960   *    *    *    * |   1    4   0    0   0   0 |   4    4   0   0  0 |  4   1  0
. x3x . . . |    6 |    3    3    0 |   * 960    *    *    * |   1    0   4    0   0   0 |   4    0   4   0  0 |  4   0  1
. x . x . . |    4 |    2    0    2 |   *   * 5760    *    * |   0    1   1    2   0   0 |   1    2   2   1  0 |  2   1  1
. . x3x . . |    6 |    0    3    3 |   *   *    * 1920    * |   0    0   2    0   2   0 |   1    0   4   0  1 |  2   0  2
. . . x3o . |    3 |    0    0    3 |   *   *    *    * 3840 |   0    0   0    2   1   1 |   0    1   2   2  1 |  1   1  2
------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x . . . ♦   12 |   12    6    0 |   4   4    0    0    0 | 240    *   *    *   *   * |   4    0   0   0  0 |  4   0  0
o3x . x . . ♦    6 |    6    0    3 |   2   0    3    0    0 |   * 1920   *    *   *   * |   1    2   0   0  0 |  2   1  0
. x3x3x . . ♦   24 |   12   12   12 |   0   4    6    4    0 |   *    * 960    *   *   * |   1    0   2   0  0 |  2   0  1
. x . x3o . ♦    6 |    3    0    6 |   0   0    3    0    2 |   *    *   * 3840   *   * |   0    1   1   1  0 |  1   1  1
. . x3x3o . ♦   12 |    0    6   12 |   0   0    0    4    4 |   *    *   *    * 960   * |   0    0   2   0  1 |  1   0  2
. . . x3o4o ♦    6 |    0    0   12 |   0   0    0    0    8 |   *    *   *    *   * 480 |   0    0   0   2  1 |  0   1  2
------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x3x . . ♦   60 |   60   30   30 |  20  20   30   10    0 |   5   10   5    0   0   0 | 192    *   *   *  * |  2   0  0
o3x . x3o . ♦    9 |    9    0    9 |   3   0    9    0    3 |   0    3   0    3   0   0 |   * 1280   *   *  * |  1   1  0
. x3x3x3o . ♦   60 |   30   30   60 |   0  10   30   20   20 |   0    0   5   10   5   0 |   *    * 384   *  * |  1   0  1
. x . x3o4o ♦   12 |    6    0   24 |   0   0   12    0   16 |   0    0   0    8   0   2 |   *    *   * 480  * |  0   1  1
. . x3x3o4o ♦   48 |    0   24   96 |   0   0    0   32   64 |   0    0   0    0  16   8 |   *    *   *   * 60 |  0   0  2
------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x3x3o . ♦  180 |  180   90  180 |  60  60  180   60   60 |  15   60  30   60  15   0 |   6   20   6   0  0 | 64   *  *
o3x . x3o4o ♦   18 |   18    0   36 |   6   0   36    0   24 |   0   12   0   24   0   3 |   0    8   0   3  0 |  * 160  *
. x3x3x3o4o ♦  480 |  240  240  960 |   0  80  480  320  640 |   0    0  80  320 160  80 |   0    0  32  40 10 |  *   * 12
```

```o3x3x3x3o4/3o

. . . . .   . | 2880 |    2    1    4 |   1   2    8    4    4 |   1    4   8    8   4   1 |   4    4   8   2  1 |  4   1  2
--------------+------+----------------+------------------------+---------------------------+---------------------+----------
. x . . .   . |    2 | 2880    *    * |   1   1    4    0    0 |   1    4   4    4   0   0 |   4    4   4   1  0 |  4   1  1
. . x . .   . |    2 |    * 1440    * |   0   2    0    4    0 |   1    0   8    0   4   0 |   4    0   8   0  1 |  4   0  2
. . . x .   . |    2 |    *    * 5760 |   0   0    2    1    2 |   0    1   2    4   2   1 |   1    2   4   2  1 |  2   1  2
--------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x . . .   . |    3 |    3    0    0 | 960   *    *    *    * |   1    4   0    0   0   0 |   4    4   0   0  0 |  4   1  0
. x3x . .   . |    6 |    3    3    0 |   * 960    *    *    * |   1    0   4    0   0   0 |   4    0   4   0  0 |  4   0  1
. x . x .   . |    4 |    2    0    2 |   *   * 5760    *    * |   0    1   1    2   0   0 |   1    2   2   1  0 |  2   1  1
. . x3x .   . |    6 |    0    3    3 |   *   *    * 1920    * |   0    0   2    0   2   0 |   1    0   4   0  1 |  2   0  2
. . . x3o   . |    3 |    0    0    3 |   *   *    *    * 3840 |   0    0   0    2   1   1 |   0    1   2   2  1 |  1   1  2
--------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x . .   . ♦   12 |   12    6    0 |   4   4    0    0    0 | 240    *   *    *   *   * |   4    0   0   0  0 |  4   0  0
o3x . x .   . ♦    6 |    6    0    3 |   2   0    3    0    0 |   * 1920   *    *   *   * |   1    2   0   0  0 |  2   1  0
. x3x3x .   . ♦   24 |   12   12   12 |   0   4    6    4    0 |   *    * 960    *   *   * |   1    0   2   0  0 |  2   0  1
. x . x3o   . ♦    6 |    3    0    6 |   0   0    3    0    2 |   *    *   * 3840   *   * |   0    1   1   1  0 |  1   1  1
. . x3x3o   . ♦   12 |    0    6   12 |   0   0    0    4    4 |   *    *   *    * 960   * |   0    0   2   0  1 |  1   0  2
. . . x3o4/3o ♦    6 |    0    0   12 |   0   0    0    0    8 |   *    *   *    *   * 480 |   0    0   0   2  1 |  0   1  2
--------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x3x .   . ♦   60 |   60   30   30 |  20  20   30   10    0 |   5   10   5    0   0   0 | 192    *   *   *  * |  2   0  0
o3x . x3o   . ♦    9 |    9    0    9 |   3   0    9    0    3 |   0    3   0    3   0   0 |   * 1280   *   *  * |  1   1  0
. x3x3x3o   . ♦   60 |   30   30   60 |   0  10   30   20   20 |   0    0   5   10   5   0 |   *    * 384   *  * |  1   0  1
. x . x3o4/3o ♦   12 |    6    0   24 |   0   0   12    0   16 |   0    0   0    8   0   2 |   *    *   * 480  * |  0   1  1
. . x3x3o4/3o ♦   48 |    0   24   96 |   0   0    0   32   64 |   0    0   0    0  16   8 |   *    *   *   * 60 |  0   0  2
--------------+------+----------------+------------------------+---------------------------+---------------------+----------
o3x3x3x3o   . ♦  180 |  180   90  180 |  60  60  180   60   60 |  15   60  30   60  15   0 |   6   20   6   0  0 | 64   *  *
o3x . x3o4/3o ♦   18 |   18    0   36 |   6   0   36    0   24 |   0   12   0   24   0   3 |   0    8   0   3  0 |  * 160  *
. x3x3x3o4/3o ♦  480 |  240  240  960 |   0  80  480  320  640 |   0    0  80  320 160  80 |   0    0  32  40 10 |  *   * 12
```

```o3x3o *b3x3x3o

. . .    . . . | 2880 |    4    1    2 |    2    2    4    8   2   1 |   1   2    4   2    4   8    4   1 |  1   2   4   2   4   2   4 |  2   1  2  2
---------------+------+----------------+-----------------------------+------------------------------------+----------------------------+-------------
. x .    . . . |    2 | 5760    *    * |    1    1    1    2   0   0 |   1   1    2   1    2   2    1   0 |  1   2   2   1   2   1   1 |  2   1  1  1
. . .    x . . |    2 |    * 1440    * |    0    0    4    0   2   0 |   0   2    0   2    0   8    0   1 |  1   0   4   0   4   0   4 |  2   0  2  2
. . .    . x . |    2 |    *    * 2880 |    0    0    0    4   1   1 |   0   0    2   0    2   4    4   1 |  0   1   2   2   2   2   4 |  1   1  2  2
---------------+------+----------------+-----------------------------+------------------------------------+----------------------------+-------------
o3x .    . . . |    3 |    3    0    0 | 1920    *    *    *   *   * |   1   1    2   0    0   0    0   0 |  1   2   2   1   0   0   0 |  2   1  1  0
. x3o    . . . |    3 |    3    0    0 |    * 1920    *    *   *   * |   1   0    0   1    2   0    0   0 |  1   2   0   0   2   1   0 |  2   1  0  1
. x . *b3x . . |    6 |    3    3    0 |    *    * 1920    *   *   * |   0   1    0   1    0   2    0   0 |  1   0   2   0   2   0   1 |  2   0  1  1
. x .    . x . |    4 |    2    0    2 |    *    *    * 5760   *   * |   0   0    1   0    1   1    1   0 |  0   1   1   1   1   1   1 |  1   1  1  1
. . .    x3x . |    6 |    0    3    3 |    *    *    *    * 960   * |   0   0    0   0    0   4    0   1 |  0   0   2   0   2   0   4 |  1   0  2  2
. . .    . x3o |    3 |    0    0    3 |    *    *    *    *   * 960 |   0   0    0   0    0   0    4   1 |  0   0   0   2   0   2   4 |  0   1  2  2
---------------+------+----------------+-----------------------------+------------------------------------+----------------------------+-------------
o3x3o    . . . ♦    6 |   12    0    0 |    4    4    0    0   0   0 | 480   *    *   *    *   *    *   * |  1   2   0   0   0   0   0 |  2   1  0  0
o3x . *b3x . . ♦   12 |   12    6    0 |    4    0    4    0   0   0 |   * 480    *   *    *   *    *   * |  1   0   2   0   0   0   0 |  2   0  1  0
o3x .    . x . ♦    6 |    6    0    3 |    2    0    0    3   0   0 |   *   * 1920   *    *   *    *   * |  0   1   1   1   0   0   0 |  1   1  1  0
. x3o *b3x . . ♦   12 |   12    6    0 |    0    4    4    0   0   0 |   *   *    * 480    *   *    *   * |  1   0   0   0   2   0   0 |  2   0  0  1
. x3o    . x . ♦    6 |    6    0    3 |    0    2    0    3   0   0 |   *   *    *   * 1920   *    *   * |  0   1   0   0   1   1   0 |  1   1  0  1
. x . *b3x3x . ♦   24 |   12   12   12 |    0    0    4    6   4   0 |   *   *    *   *    * 960    *   * |  0   0   1   0   1   0   1 |  1   0  1  1
. x .    . x3o ♦    6 |    3    0    6 |    0    0    0    3   0   2 |   *   *    *   *    *   * 1920   * |  0   0   0   1   0   1   1 |  0   1  1  1
. . .    x3x3o ♦   12 |    0    6   12 |    0    0    0    0   4   4 |   *   *    *   *    *   *    * 240 |  0   0   0   0   0   0   4 |  0   0  1  1
---------------+------+----------------+-----------------------------+------------------------------------+----------------------------+-------------
o3x3o *b3x . . ♦   48 |   96   24    0 |   32   32   32    0   0   0 |   8   8    0   8    0   0    0   0 | 60   *   *   *   *   *   * |  2   0  0  0
o3x3o    . x . ♦   12 |   24    0    6 |    8    8    0   12   0   0 |   2   0    4   0    4   0    0   0 |  * 480   *   *   *   *   * |  1   1  0  0
o3x . *b3x3x . ♦   60 |   60   30   30 |   20    0   20   30  10   0 |   0   5   10   0    0   5    0   0 |  *   * 192   *   *   *   * |  1   0  1  0
o3x .    . x3o ♦    9 |    9    0    9 |    3    0    0    9   0   3 |   0   0    3   0    0   0    3   0 |  *   *   * 640   *   *   * |  0   1  1  0
. x3o *b3x3x . ♦   60 |   60   30   30 |    0   20   20   30  10   0 |   0   0    0   5   10   5    0   0 |  *   *   *   * 192   *   * |  1   0  0  1
. x3o    . x3o ♦    9 |    9    0    9 |    0    3    0    9   0   3 |   0   0    0   0    3   0    3   0 |  *   *   *   *   * 640   * |  0   1  0  1
. x . *b3x3x3o ♦   60 |   30   30   60 |    0    0   10   30  20  20 |   0   0    0   0    0   5   10   5 |  *   *   *   *   *   * 192 |  0   0  1  1
---------------+------+----------------+-----------------------------+------------------------------------+----------------------------+-------------
o3x3o *b3x3x . ♦  480 |  960  240  240 |  320  320  320  480  80   0 |  80  80  160  80  160  80    0   0 | 10  40  16   0  16   0   0 | 12   *  *  *
o3x3o    . x3o ♦   18 |   36    0   18 |   12   12    0   36   0   6 |   3   0   12   0   12   0   12   0 |  0   3   0   4   0   4   0 |  * 160  *  *
o3x . *b3x3x3o ♦  180 |  180   90  180 |   60    0   60  180  60  60 |   0  15   60   0    0  30   60  15 |  0   0   6  20   0   0   6 |  *   * 32  *
. x3o *b3x3x3o ♦  180 |  180   90  180 |    0   60   60  180  60  60 |   0   0    0  15   60  30   60  15 |  0   0   0   0   6  20   6 |  *   *  * 32
```