Acronym spog Name small prismatohexacontitetrapeton,runcinated hexacross Circumradius sqrt(7/2) = 1.870829 Coordinates (sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign Externallinks

Incidence matrix according to Dynkin symbol

```x3o3o3x3o4o

. . . . . . | 960 |    3   12 |   3   24   12   12 |   1   12   12   24   4   12   3 |   4   12  12   6   4   3 |  4   3  3  1
------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x . . . . . |   2 | 1440    * |   2    8    0    0 |   1    8    4    2   0    0   0 |   4    8   4   2   0   0 |  4   2  1  0
. . . x . . |   2 |    * 5760 |   0    2    2    2 |   0    1    2    4   1    4   1 |   1    2   4   2   2   2 |  2   1  2  1
------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o . . . . |   3 |    3    0 | 960    *    *    * |   1    4    0    0   0    0   0 |   4    4   0   0   0   0 |  4   1  0  0
x . . x . . |   4 |    2    2 |   * 5760    *    * |   0    1    1    2   0    0   0 |   1    2   2   1   0   0 |  2   1  1  0
. . o3x . . |   3 |    0    3 |   *    * 3840    * |   0    0    1    0   1    2   0 |   1    0   2   0   2   1 |  2   0  1  1
. . . x3o . |   3 |    0    3 |   *    *    * 3840 |   0    0    0    2   0    2   1 |   0    1   2   2   1   2 |  1   1  2  1
------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o . . . ♦   4 |    6    0 |   4    0    0    0 | 240    *    *    *   *    *   * |   4    0   0   0   0   0 |  4   0  0  0
x3o . x . . ♦   6 |    6    3 |   2    3    0    0 |   * 1920    *    *   *    *   * |   1    2   0   0   0   0 |  2   1  0  0
x . o3x . . ♦   6 |    3    6 |   0    3    2    0 |   *    * 1920    *   *    *   * |   1    0   2   0   0   0 |  2   0  1  0
x . . x3o . ♦   6 |    3    6 |   0    3    0    2 |   *    *    * 3840   *    *   * |   0    1   1   1   0   0 |  1   1  1  0
. o3o3x . . ♦   4 |    0    6 |   0    0    4    0 |   *    *    *    * 960    *   * |   1    0   0   0   2   0 |  2   0  0  1
. . o3x3o . ♦   6 |    0   12 |   0    0    4    4 |   *    *    *    *   * 1920   * |   0    0   1   0   1   1 |  1   0  1  1
. . . x3o4o ♦   6 |    0   12 |   0    0    0    8 |   *    *    *    *   *    * 480 |   0    0   0   2   0   2 |  0   1  2  1
------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o3x . . ♦  20 |   30   30 |  20   30   20    0 |   5   10   10    0   5    0   0 | 192    *   *   *   *   * |  2   0  0  0
x3o . x3o . ♦   9 |    9    9 |   3    9    0    3 |   0    3    0    3   0    0   0 |   * 1280   *   *   *   * |  1   1  0  0
x . o3x3o . ♦  12 |    6   24 |   0   12    8    8 |   0    0    4    4   0    2   0 |   *    * 960   *   *   * |  1   0  1  0
x . . x3o4o ♦  12 |    6   24 |   0   12    0   16 |   0    0    0    8   0    0   2 |   *    *   * 480   *   * |  0   1  1  0
. o3o3x3o . ♦  10 |    0   30 |   0    0   20   10 |   0    0    0    0   5    5   0 |   *    *   *   * 384   * |  1   0  0  1
. . o3x3o4o ♦  24 |    0   96 |   0    0   32   64 |   0    0    0    0   0   16   8 |   *    *   *   *   * 120 |  0   0  1  1
------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o3x3o . ♦  60 |   90  180 |  60  180  120   60 |  15   60   60   60  30   30   0 |   6   20  15   0   6   0 | 64   *  *  *
x3o . x3o4o ♦  18 |   18   36 |   6   36    0   24 |   0   12    0   24   0    0   3 |   0    8   0   3   0   0 |  * 160  *  *
x . o3x3o4o ♦  48 |   24  192 |   0   96   64  128 |   0    0   32   64   0   32  16 |   0    0  16   8   0   2 |  *   * 60  *
. o3o3x3o4o ♦  80 |    0  480 |   0    0  320  320 |   0    0    0    0  80  160  40 |   0    0   0   0  32  10 |  *   *  * 12
```

```x3o3o3x3o4/3o

. . . . .   . | 960 |    3   12 |   3   24   12   12 |   1   12   12   24   4   12   3 |   4   12  12   6   4   3 |  4   3  3  1
--------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x . . . .   . |   2 | 1440    * |   2    8    0    0 |   1    8    4    2   0    0   0 |   4    8   4   2   0   0 |  4   2  1  0
. . . x .   . |   2 |    * 5760 |   0    2    2    2 |   0    1    2    4   1    4   1 |   1    2   4   2   2   2 |  2   1  2  1
--------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o . . .   . |   3 |    3    0 | 960    *    *    * |   1    4    0    0   0    0   0 |   4    4   0   0   0   0 |  4   1  0  0
x . . x .   . |   4 |    2    2 |   * 5760    *    * |   0    1    1    2   0    0   0 |   1    2   2   1   0   0 |  2   1  1  0
. . o3x .   . |   3 |    0    3 |   *    * 3840    * |   0    0    1    0   1    2   0 |   1    0   2   0   2   1 |  2   0  1  1
. . . x3o   . |   3 |    0    3 |   *    *    * 3840 |   0    0    0    2   0    2   1 |   0    1   2   2   1   2 |  1   1  2  1
--------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o . .   . ♦   4 |    6    0 |   4    0    0    0 | 240    *    *    *   *    *   * |   4    0   0   0   0   0 |  4   0  0  0
x3o . x .   . ♦   6 |    6    3 |   2    3    0    0 |   * 1920    *    *   *    *   * |   1    2   0   0   0   0 |  2   1  0  0
x . o3x .   . ♦   6 |    3    6 |   0    3    2    0 |   *    * 1920    *   *    *   * |   1    0   2   0   0   0 |  2   0  1  0
x . . x3o   . ♦   6 |    3    6 |   0    3    0    2 |   *    *    * 3840   *    *   * |   0    1   1   1   0   0 |  1   1  1  0
. o3o3x .   . ♦   4 |    0    6 |   0    0    4    0 |   *    *    *    * 960    *   * |   1    0   0   0   2   0 |  2   0  0  1
. . o3x3o   . ♦   6 |    0   12 |   0    0    4    4 |   *    *    *    *   * 1920   * |   0    0   1   0   1   1 |  1   0  1  1
. . . x3o4/3o ♦   6 |    0   12 |   0    0    0    8 |   *    *    *    *   *    * 480 |   0    0   0   2   0   2 |  0   1  2  1
--------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o3x .   . ♦  20 |   30   30 |  20   30   20    0 |   5   10   10    0   5    0   0 | 192    *   *   *   *   * |  2   0  0  0
x3o . x3o   . ♦   9 |    9    9 |   3    9    0    3 |   0    3    0    3   0    0   0 |   * 1280   *   *   *   * |  1   1  0  0
x . o3x3o   . ♦  12 |    6   24 |   0   12    8    8 |   0    0    4    4   0    2   0 |   *    * 960   *   *   * |  1   0  1  0
x . . x3o4/3o ♦  12 |    6   24 |   0   12    0   16 |   0    0    0    8   0    0   2 |   *    *   * 480   *   * |  0   1  1  0
. o3o3x3o   . ♦  10 |    0   30 |   0    0   20   10 |   0    0    0    0   5    5   0 |   *    *   *   * 384   * |  1   0  0  1
. . o3x3o4/3o ♦  24 |    0   96 |   0    0   32   64 |   0    0    0    0   0   16   8 |   *    *   *   *   * 120 |  0   0  1  1
--------------+-----+-----------+--------------------+---------------------------------+--------------------------+-------------
x3o3o3x3o   . ♦  60 |   90  180 |  60  180  120   60 |  15   60   60   60  30   30   0 |   6   20  15   0   6   0 | 64   *  *  *
x3o . x3o4/3o ♦  18 |   18   36 |   6   36    0   24 |   0   12    0   24   0    0   3 |   0    8   0   3   0   0 |  * 160  *  *
x . o3x3o4/3o ♦  48 |   24  192 |   0   96   64  128 |   0    0   32   64   0   32  16 |   0    0  16   8   0   2 |  *   * 60  *
. o3o3x3o4/3o ♦  80 |    0  480 |   0    0  320  320 |   0    0    0    0  80  160  40 |   0    0   0   0  32  10 |  *   *  * 12
```

```. . .    . . . | 960 |   12    3 |    6    6   12   24   3 |   3   6   12   6   12   4   12   12   1 |   3   6   2   6   6   2   6   6   4 |  1  3   3  2  2
---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+----------------
. x .    . . . |   2 | 5760    * |    1    1    2    2   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 |    * 1440 |    0    0    0    8   2 |   0   0    4   0    4   0    4    8   1 |   0   2   0   2   4   0   2   4   4 |  0  1   2  2  2
---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+----------------
o3x .    . . . |   3 |    3    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 |    * 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 . *b3o . . |   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    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
. . .    . o3x |   3 |    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 |    4    4    0    0   0 | 480   *    *   *    *   *    *    *   * |   2   2   0   0   0   0   0   0   0 |  1  2   1  0  0
o3x . *b3o . . ♦   6 |   12    0 |    4    0    4    0   0 |   * 960    *   *    *   *    *    *   * |   1   0   1   1   0   0   0   0   0 |  1  1   0  1  0
o3x .    . . x ♦   6 |    6    3 |    2    0    0    3   0 |   *   * 1920   *    *   *    *    *   * |   0   1   0   1   1   0   0   0   0 |  0  1   1  1  0
. x3o *b3o . . ♦   6 |   12    0 |    0    4    4    0   0 |   *   *    * 960    *   *    *    *   * |   1   0   0   0   0   1   1   0   0 |  1  1   0  0  1
. x3o    . . x ♦   6 |    6    3 |    0    2    0    3   0 |   *   *    *   * 1920   *    *    *   * |   0   1   0   0   0   0   1   1   0 |  0  1   1  0  1
. x . *b3o3o . ♦   4 |    6    0 |    0    0    4    0   0 |   *   *    *   *    * 960    *    *   * |   0   0   1   0   0   1   0   0   1 |  1  0   0  1  1
. x . *b3o . x ♦   6 |    6    3 |    0    0    2    3   0 |   *   *    *   *    *   * 1920    *   * |   0   0   0   1   0   0   1   0   1 |  0  1   0  1  1
. x .    . o3x ♦   6 |    3    6 |    0    0    0    3   2 |   *   *    *   *    *   *    * 1920   * |   0   0   0   0   1   0   0   1   1 |  0  0   1  1  1
. . .    o3o3x ♦   4 |    0    6 |    0    0    0    0   4 |   *   *    *   *    *   *    *    * 240 |   0   0   0   0   0   0   0   0   4 |  0  0   0  2  2
---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+----------------
o3x3o *b3o . . ♦  24 |   96    0 |   32   32   32    0   0 |   8   8    0   8    0   0    0    0   0 | 120   *   *   *   *   *   *   *   * |  1  1   0  0  0
o3x3o    . . x ♦  12 |   24    6 |    8    8    0   12   0 |   2   0    4   0    4   0    0    0   0 |   * 480   *   *   *   *   *   *   * |  0  1   1  0  0
o3x . *b3o3o . ♦  10 |   30    0 |   10    0   20    0   0 |   0   5    0   0    0   5    0    0   0 |   *   * 192   *   *   *   *   *   * |  1  0   0  1  0
o3x . *b3o . x ♦  12 |   24    6 |    8    0    8   12   0 |   0   2    4   0    0   0    4    0   0 |   *   *   * 480   *   *   *   *   * |  0  1   0  1  0
o3x .    . o3x ♦   9 |    9    9 |    3    0    0    9   3 |   0   0    3   0    0   0    0    3   0 |   *   *   *   * 640   *   *   *   * |  0  0   1  1  0
. x3o *b3o3o . ♦  10 |   30    0 |    0   10   20    0   0 |   0   0    0   5    0   5    0    0   0 |   *   *   *   *   * 192   *   *   * |  1  0   0  0  1
. x3o *b3o . x ♦  12 |   24    6 |    0    8    8   12   0 |   0   0    0   2    4   0    4    0   0 |   *   *   *   *   *   * 480   *   * |  0  1   0  0  1
. x3o    . o3x ♦   9 |    9    9 |    0    3    0    9   3 |   0   0    0   0    3   0    0    3   0 |   *   *   *   *   *   *   * 640   * |  0  0   1  0  1
. x . *b3o3o3x ♦  20 |   30   30 |    0    0   20   30  20 |   0   0    0   0    0   5   10   10   5 |   *   *   *   *   *   *   *   * 192 |  0  0   0  1  1
---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+----------------
o3x3o *b3o3o . ♦  80 |  480    0 |  160  160  320    0   0 |  40  80    0  80    0  80    0    0   0 |  10   0  16   0   0  16   0   0   0 | 12  *   *  *  *
o3x3o *b3o . x ♦  48 |  192   24 |   64   64   64   96   0 |  16  16   32  16   32   0   32    0   0 |   2   8   0   8   0   0   8   0   0 |  * 60   *  *  *
o3x3o    . o3x ♦  18 |   36   18 |   12   12    0   36   6 |   3   0   12   0   12   0    0   12   0 |   0   3   0   0   4   0   0   4   0 |  *  * 160  *  *
o3x . *b3o3o3x ♦  60 |  180   90 |   60    0  120  180  60 |   0  30   60   0    0  30   60   60  15 |   0   0   6  15  20   0   0   0   6 |  *  *   * 32  *
. x3o *b3o3o3x ♦  60 |  180   90 |    0   60  120  180  60 |   0   0    0  30   60  30   60   60  15 |   0   0   0   0   0   6  15  20   6 |  *  *   *  * 32
```