Acronym scag Name small cellihexacontitetrapeton,stericated hexacross Circumradius 2 Coordinates (sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign Externallinks

Incidence matrix according to Dynkin symbol

```x3o3o3o3x4o

. . . . . . | 960 |    4    8 |    6   12   12   4 |   4   24   24   12    8   6 |   1   8   12  12   8  12   2   4 |  2   4   6  4  1
------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x . . . . . |   2 | 1920    * |    3    6    0   0 |   3   12    6    3    0   0 |   1   6    6   6   2   3   0   0 |  2   3   3  1  0
. . . . x . |   2 |    * 3840 |    0    3    3   1 |   0    3    6    3    3   3 |   0   1    3   3   3   6   1   3 |  1   1   3  3  1
------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o . . . . |   3 |    3    0 | 1920    *    *   * |   2    4    0    0    0   0 |   1   4    2   2   0   0   0   0 |  2   2   1  0  0
x . . . x . |   4 |    2    2 |    * 5760    *   * |   0    2    2    1    0   0 |   0   1    2   2   1   2   0   0 |  1   1   2  1  0
. . . o3x . |   3 |    0    3 |    *    * 3840   * |   0    0    2    0    2   1 |   0   0    1   0   2   2   1   2 |  1   0   1  2  1
. . . . x4o |   4 |    0    4 |    *    *    * 960 |   0    0    0    3    0   3 |   0   0    0   3   0   6   0   3 |  0   1   3  3  1
------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o . . . ♦   4 |    6    0 |    4    0    0   0 | 960    *    *    *    *   * |   1   2    0   0   0   0   0   0 |  2   1   0  0  0
x3o . . x . ♦   6 |    6    3 |    2    3    0   0 |   * 3840    *    *    *   * |   0   1    1   1   0   0   0   0 |  1   1   1  0  0
x . . o3x . ♦   6 |    3    6 |    0    3    2   0 |   *    * 3840    *    *   * |   0   0    1   0   1   1   0   0 |  1   0   1  1  0
x . . . x4o ♦   8 |    4    8 |    0    4    0   2 |   *    *    * 1440    *   * |   0   0    0   2   0   2   0   0 |  0   1   2  1  0
. . o3o3x . ♦   4 |    0    6 |    0    0    4   0 |   *    *    *    * 1920   * |   0   0    0   0   1   0   1   1 |  1   0   0  1  1
. . . o3x4o ♦  12 |    0   24 |    0    0    8   6 |   *    *    *    *    * 480 |   0   0    0   0   0   2   0   2 |  0   0   1  2  1
------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o3o . . ♦   5 |   10    0 |   10    0    0   0 |   5    0    0    0    0   0 | 192   *    *   *   *   *   *   * |  2   0   0  0  0
x3o3o . x . ♦   8 |   12    4 |    8    6    0   0 |   2    4    0    0    0   0 |   * 960    *   *   *   *   *   * |  1   1   0  0  0
x3o . o3x . ♦   9 |    9    9 |    3    9    3   0 |   0    3    3    0    0   0 |   *   * 1280   *   *   *   *   * |  1   0   1  0  0
x3o . . x4o ♦  12 |   12   12 |    4   12    0   3 |   0    4    0    3    0   0 |   *   *    * 960   *   *   *   * |  0   1   1  0  0
x . o3o3x . ♦   8 |    4   12 |    0    6    8   0 |   0    0    4    0    2   0 |   *   *    *   * 960   *   *   * |  1   0   0  1  0
x . . o3x4o ♦  24 |   12   48 |    0   24   16  12 |   0    0    8    6    0   2 |   *   *    *   *   * 480   *   * |  0   0   1  1  0
. o3o3o3x . ♦   5 |    0   10 |    0    0   10   0 |   0    0    0    0    5   0 |   *   *    *   *   *   * 384   * |  1   0   0  0  1
. . o3o3x4o ♦  32 |    0   96 |    0    0   64  24 |   0    0    0    0   16   8 |   *   *    *   *   *   *   * 120 |  0   0   0  1  1
------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o3o3x . ♦  30 |   60   60 |   60   90   60   0 |  30   60   60    0   30   0 |   6  15   20   0  15   0   6   0 | 64   *   *  *  *
x3o3o . x4o ♦  16 |   24   16 |   16   24    0   4 |   4   16    0    6    0   0 |   0   4    0   4   0   0   0   0 |  * 240   *  *  *
x3o . o3x4o ♦  36 |   36   72 |   12   72   24  18 |   0   24   24   18    0   3 |   0   0    8   6   0   3   0   0 |  *   * 160  *  *
x . o3o3x4o ♦  64 |   32  192 |    0   96  128  48 |   0    0   64   24   32  16 |   0   0    0   0  16   8   0   2 |  *   *   * 60  *
. o3o3o3x4o ♦  80 |    0  320 |    0    0  320  80 |   0    0    0    0  160  40 |   0   0    0   0   0   0  32  10 |  *   *   *  * 12
```

```x3o3o3o3x4/3o

. . . . .   . | 960 |    4    8 |    6   12   12   4 |   4   24   24   12    8   6 |   1   8   12  12   8  12   2   4 |  2   4   6  4  1
--------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x . . . .   . |   2 | 1920    * |    3    6    0   0 |   3   12    6    3    0   0 |   1   6    6   6   2   3   0   0 |  2   3   3  1  0
. . . . x   . |   2 |    * 3840 |    0    3    3   1 |   0    3    6    3    3   3 |   0   1    3   3   3   6   1   3 |  1   1   3  3  1
--------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o . . .   . |   3 |    3    0 | 1920    *    *   * |   2    4    0    0    0   0 |   1   4    2   2   0   0   0   0 |  2   2   1  0  0
x . . . x   . |   4 |    2    2 |    * 5760    *   * |   0    2    2    1    0   0 |   0   1    2   2   1   2   0   0 |  1   1   2  1  0
. . . o3x   . |   3 |    0    3 |    *    * 3840   * |   0    0    2    0    2   1 |   0   0    1   0   2   2   1   2 |  1   0   1  2  1
. . . . x4/3o |   4 |    0    4 |    *    *    * 960 |   0    0    0    3    0   3 |   0   0    0   3   0   6   0   3 |  0   1   3  3  1
--------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o . .   . ♦   4 |    6    0 |    4    0    0   0 | 960    *    *    *    *   * |   1   2    0   0   0   0   0   0 |  2   1   0  0  0
x3o . . x   . ♦   6 |    6    3 |    2    3    0   0 |   * 3840    *    *    *   * |   0   1    1   1   0   0   0   0 |  1   1   1  0  0
x . . o3x   . ♦   6 |    3    6 |    0    3    2   0 |   *    * 3840    *    *   * |   0   0    1   0   1   1   0   0 |  1   0   1  1  0
x . . . x4/3o ♦   8 |    4    8 |    0    4    0   2 |   *    *    * 1440    *   * |   0   0    0   2   0   2   0   0 |  0   1   2  1  0
. . o3o3x   . ♦   4 |    0    6 |    0    0    4   0 |   *    *    *    * 1920   * |   0   0    0   0   1   0   1   1 |  1   0   0  1  1
. . . o3x4/3o ♦  12 |    0   24 |    0    0    8   6 |   *    *    *    *    * 480 |   0   0    0   0   0   2   0   2 |  0   0   1  2  1
--------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o3o .   . ♦   5 |   10    0 |   10    0    0   0 |   5    0    0    0    0   0 | 192   *    *   *   *   *   *   * |  2   0   0  0  0
x3o3o . x   . ♦   8 |   12    4 |    8    6    0   0 |   2    4    0    0    0   0 |   * 960    *   *   *   *   *   * |  1   1   0  0  0
x3o . o3x   . ♦   9 |    9    9 |    3    9    3   0 |   0    3    3    0    0   0 |   *   * 1280   *   *   *   *   * |  1   0   1  0  0
x3o . . x4/3o ♦  12 |   12   12 |    4   12    0   3 |   0    4    0    3    0   0 |   *   *    * 960   *   *   *   * |  0   1   1  0  0
x . o3o3x   . ♦   8 |    4   12 |    0    6    8   0 |   0    0    4    0    2   0 |   *   *    *   * 960   *   *   * |  1   0   0  1  0
x . . o3x4/3o ♦  24 |   12   48 |    0   24   16  12 |   0    0    8    6    0   2 |   *   *    *   *   * 480   *   * |  0   0   1  1  0
. o3o3o3x   . ♦   5 |    0   10 |    0    0   10   0 |   0    0    0    0    5   0 |   *   *    *   *   *   * 384   * |  1   0   0  0  1
. . o3o3x4/3o ♦  32 |    0   96 |    0    0   64  24 |   0    0    0    0   16   8 |   *   *    *   *   *   *   * 120 |  0   0   0  1  1
--------------+-----+-----------+--------------------+-----------------------------+----------------------------------+-----------------
x3o3o3o3x   . ♦  30 |   60   60 |   60   90   60   0 |  30   60   60    0   30   0 |   6  15   20   0  15   0   6   0 | 64   *   *  *  *
x3o3o . x4/3o ♦  16 |   24   16 |   16   24    0   4 |   4   16    0    6    0   0 |   0   4    0   4   0   0   0   0 |  * 240   *  *  *
x3o . o3x4/3o ♦  36 |   36   72 |   12   72   24  18 |   0   24   24   18    0   3 |   0   0    8   6   0   3   0   0 |  *   * 160  *  *
x . o3o3x4/3o ♦  64 |   32  192 |    0   96  128  48 |   0    0   64   24   32  16 |   0   0    0   0  16   8   0   2 |  *   *   * 60  *
. o3o3o3x4/3o ♦  80 |    0  320 |    0    0  320  80 |   0    0    0    0  160  40 |   0   0    0   0   0   0  32  10 |  *   *   *  * 12
```

```x3o3x *b3o3o3x

. . .    . . . | 960 |    4    4    4 |    6   4   12    6   12    6 |   6   4   12   12   12   4   12   12   4 |   4  12   1   4   6  12   4   1   4   6   1   4 |  1  4   6  1   4  1
---------------+-----+----------------+------------------------------+------------------------------------------+-------------------------------------------------+--------------------
x . .    . . . |   2 | 1920    *    * |    3   1    3    0    0    0 |   3   3    6    3    3   0    0    0   0 |   3   6   1   3   3   3   1   0   0   0   0   0 |  1  3   3  1   1  0
. . x    . . . |   2 |    * 1920    * |    0   1    0    3    3    0 |   3   0    0    3    0   3    6    3   0 |   3   6   0   0   0   3   0   1   3   3   0   1 |  1  3   3  0   1  1
. . .    . . x |   2 |    *    * 1920 |    0   0    3    0    3    3 |   0   0    3    3    6   0    3    6   3 |   0   3   0   1   3   6   3   0   1   3   1   3 |  0  1   3  1   3  1
---------------+-----+----------------+------------------------------+------------------------------------------+-------------------------------------------------+--------------------
x3o .    . . . |   3 |    3    0    0 | 1920   *    *    *    *    * |   1   2    2    0    0   0    0    0   0 |   2   2   1   2   1   0   0   0   0   0   0   0 |  1  2   1  1   0  0
x . x    . . . |   4 |    2    2    0 |    * 960    *    *    *    * |   3   0    0    3    0   0    0    0   0 |   3   6   0   0   0   3   0   0   0   0   0   0 |  1  3   3  0   3  0
x . .    . . x |   4 |    2    0    2 |    *   * 2880    *    *    * |   0   0    2    1    2   0    0    0   0 |   0   2   0   1   2   2   1   0   0   0   0   0 |  0  1   2  1   1  0
. o3x    . . . |   3 |    0    3    0 |    *   *    * 1920    *    * |   1   0    0    0    0   2    2    0   0 |   2   2   0   0   0   0   0   1   2   1   0   0 |  1  2   1  0   0  1
. . x    . . x |   4 |    0    2    2 |    *   *    *    * 2880    * |   0   0    0    1    0   0    2    2   0 |   0   2   0   0   0   2   0   0   1   2   0   1 |  0  1   2  0   1  1
. . .    . o3x |   3 |    0    0    3 |    *   *    *    *    * 1920 |   0   0    0    0    2   0    0    2   2 |   0   0   0   0   1   2   2   0   0   1   1   2 |  0  0   1  1   2  1
---------------+-----+----------------+------------------------------+------------------------------------------+-------------------------------------------------+--------------------
x3o3x    . . . ♦  12 |   12   12    0 |    4   6    0    4    0    0 | 480   *    *    *    *   *    *    *   * |   2   2   0   0   0   0   0   0   0   0   0   0 |  1  2   1  0   0  0
x3o . *b3o . . ♦   4 |    6    0    0 |    4   0    0    0    0    0 |   * 960    *    *    *   *    *    *   * |   1   0   1   1   0   0   0   0   0   0   0   0 |  1  1   0  1   0  0
x3o .    . . x ♦   6 |    6    0    3 |    2   0    3    0    0    0 |   *   * 1920    *    *   *    *    *   * |   0   1   0   1   1   0   0   0   0   0   0   0 |  0  1   1  1   0  0
x . x    . . x ♦   8 |    4    4    4 |    0   2    2    0    2    0 |   *   *    * 1440    *   *    *    *   * |   0   2   0   0   0   2   0   0   0   0   0   0 |  0  1   1  0   1  0
x . .    . o3x ♦   6 |    3    0    6 |    0   0    3    0    0    2 |   *   *    *    * 1920   *    *    *   * |   0   0   0   0   1   1   1   0   0   0   0   0 |  0  0   1  1   1  0
. o3x *b3o . . ♦   4 |    0    6    0 |    0   0    0    4    0    0 |   *   *    *    *    * 960    *    *   * |   1   0   0   0   0   0   0   1   1   0   0   0 |  1  1   0  0   0  1
. o3x    . . x ♦   6 |    0    6    3 |    0   0    0    2    3    0 |   *   *    *    *    *   * 1920    *   * |   0   1   0   0   0   0   0   0   1   1   0   0 |  0  1   1  0   0  1
. . x    . o3x ♦   6 |    0    3    6 |    0   0    0    0    3    2 |   *   *    *    *    *   *    * 1920   * |   0   0   0   0   0   1   0   0   0   1   0   1 |  0  0   1  0   1  1
. . .    o3o3x ♦   4 |    0    0    6 |    0   0    0    0    0    4 |   *   *    *    *    *   *    *    * 960 |   0   0   0   0   0   0   1   0   0   0   1   1 |  0  0   0  1   1  1
---------------+-----+----------------+------------------------------+------------------------------------------+-------------------------------------------------+--------------------
x3o3x *b3o . . ♦  32 |   48   48    0 |   32  24    0   32    0    0 |   8   8    0    0    0   8    0    0   0 | 120   *   *   *   *   *   *   *   *   *   *   * |  1  1   0  0   0  0
x3o3x    . . x ♦  24 |   24   24   12 |    8  12   12    8   12    0 |   2   0    4    6    0   0    4    0   0 |   * 480   *   *   *   *   *   *   *   *   *   * |  0  1   1  0   0  0
x3o . *b3o3o . ♦   5 |   10    0    0 |   10   0    0    0    0    0 |   0   5    0    0    0   0    0    0   0 |   *   * 192   *   *   *   *   *   *   *   *   * |  1  0   0  1   0  0
x3o . *b3o . x ♦   8 |   12    0    4 |    8   0    6    0    0    0 |   0   2    4    0    0   0    0    0   0 |   *   *   * 480   *   *   *   *   *   *   *   * |  0  1   0  1   0  0
x3o .    . o3x ♦   9 |    9    0    9 |    3   0    9    0    0    3 |   0   0    3    0    3   0    0    0   0 |   *   *   *   * 640   *   *   *   *   *   *   * |  0  0   1  1   0  0
x . x    . o3x ♦  12 |    6    6   12 |    0   3    6    0    6    4 |   0   0    0    3    2   0    0    2   0 |   *   *   *   *   * 960   *   *   *   *   *   * |  0  0   1  0   1  0
x . .    o3o3x ♦   8 |    4    0   12 |    0   0    6    0    0    8 |   0   0    0    0    4   0    0    0   2 |   *   *   *   *   *   * 480   *   *   *   *   * |  0  0   0  1   1  0
. o3x *b3o3o . ♦   5 |    0   10    0 |    0   0    0   10    0    0 |   0   0    0    0    0   5    0    0   0 |   *   *   *   *   *   *   * 192   *   *   *   * |  1  0   0  0   0  1
. o3x *b3o . x ♦   8 |    0   12    4 |    0   0    0    8    6    0 |   0   0    0    0    0   2    4    0   0 |   *   *   *   *   *   *   *   * 480   *   *   * |  0  1   0  0   0  1
. o3x    . o3x ♦   9 |    0    9    9 |    0   0    0    3    9    3 |   0   0    0    0    0   0    3    3   0 |   *   *   *   *   *   *   *   *   * 640   *   * |  0  0   1  0   0  1
. o . *b3o3o3x ♦   5 |    0    0   10 |    0   0    0    0    0   10 |   0   0    0    0    0   0    0    0   5 |   *   *   *   *   *   *   *   *   *   * 192   * |  0  0   0  1   0  1
. . x    o3o3x ♦   8 |    0    4   12 |    0   0    0    0    6    8 |   0   0    0    0    0   0    0    4   2 |   *   *   *   *   *   *   *   *   *   *   * 480 |  0  0   0  0   1  1
---------------+-----+----------------+------------------------------+------------------------------------------+-------------------------------------------------+--------------------
x3o3x *b3o3o . ♦  80 |  160  160    0 |  160  80    0  160    0    0 |  40  80    0    0    0  80    0    0   0 |  10   0  16   0   0   0   0  16   0   0   0   0 | 12  *   *  *   *  *
x3o3x *b3o . x ♦  64 |   96   96   32 |   64  48   48   64   48    0 |  16  16   32   24    0  16   32    0   0 |   2   8   0   8   0   0   0   0   8   0   0   0 |  * 60   *  *   *  *
x3o3x    . o3x ♦  36 |   36   36   36 |   12  18   36   12   36   12 |   3   0   12   18   12   0   12   12   0 |   0   3   0   0   4   6   0   0   0   4   0   0 |  *  * 160  *   *  *
x3o . *b3o3o3x ♦  30 |   60    0   60 |   60   0   90    0    0   60 |   0  30   60    0   60   0    0    0  30 |   0   0   6  15  20   0  15   0   0   0   6   0 |  *  *   * 32   *  *
x . x    o3o3x ♦  16 |    8    8   24 |    0   4   12    0   12   16 |   0   0    0    6    8   0    0    8   4 |   0   0   0   0   0   4   2   0   0   0   0   2 |  *  *   *  * 240  *
. o3x *b3o3o3x ♦  30 |    0   60   60 |    0   0    0   60   90   60 |   0   0    0    0    0  30   60   60  30 |   0   0   0   0   0   0   0   6  15  20   6  15 |  *  *   *  *   * 32
```

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