Acronym saborx
Name small birhombated hexeract,
bicantellated hexeract
Circumradius sqrt(7) = 2.645751
Coordinates (sqrt(2), sqrt(2), sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

o3o3x3o3x4o

. . . . . . | 1920 |    6    4 |    6    3   12    2   2 |   2   3   12   6    6   1 |   1   4   6   6  3 |  2   2  3
------------+------+-----------+-------------------------+---------------------------+--------------------+----------
. . x . . . |    2 | 5760    * |    2    1    2    0   0 |   1   2    4   2    1   0 |   1   2   4   2  1 |  2   1  2
. . . . x . |    2 |    * 3840 |    0    0    3    1   1 |   0   0    3   3    3   1 |   0   1   3   3  3 |  1   1  3
------------+------+-----------+-------------------------+---------------------------+--------------------+----------
. o3x . . . |    3 |    3    0 | 3840    *    *    *   * |   1   1    2   0    0   0 |   1   2   2   1  0 |  2   1  1
. . x3o . . |    3 |    3    0 |    * 1920    *    *   * |   0   2    0   2    0   0 |   1   0   4   0  1 |  2   0  2
. . x . x . |    4 |    2    2 |    *    * 5760    *   * |   0   0    2   1    1   0 |   0   1   2   2  1 |  1   1  2
. . . o3x . |    3 |    0    3 |    *    *    * 1280   * |   0   0    0   3    0   1 |   0   0   3   0  3 |  1   0  3
. . . . x4o |    4 |    0    4 |    *    *    *    * 960 |   0   0    0   0    3   1 |   0   0   0   3  3 |  0   1  3
------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x . . .     4 |    6    0 |    4    0    0    0   0 | 960   *    *   *    *   * |   1   2   0   0  0 |  2   1  0
. o3x3o . .     6 |   12    0 |    4    4    0    0   0 |   * 960    *   *    *   * |   1   0   2   0  0 |  2   0  1
. o3x . x .     6 |    6    3 |    2    0    3    0   0 |   *   * 3840   *    *   * |   0   1   1   1  0 |  1   1  1
. . x3o3x .    12 |   12   12 |    0    4    6    4   0 |   *   *    * 960    *   * |   0   0   2   0  1 |  1   0  2
. . x . x4o     8 |    4    8 |    0    0    4    0   2 |   *   *    *   * 1440   * |   0   0   0   2  1 |  0   1  2
. . . o3x4o    12 |    0   24 |    0    0    0    8   6 |   *   *    *   *    * 160 |   0   0   0   0  3 |  0   0  3
------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x3o . .    10 |   30    0 |   20   10    0    0   0 |   5   5    0   0    0   0 | 192   *   *   *  * |  2   0  0
o3o3x . x .     8 |   12    4 |    8    0    6    0   0 |   2   0    4   0    0   0 |   * 960   *   *  * |  1   1  0
. o3x3o3x .    30 |   60   30 |   20   20   30   10   0 |   0   5   10   5    0   0 |   *   * 384   *  * |  1   0  1
. o3x . x4o    12 |   12   12 |    4    0   12    0   3 |   0   0    4   0    3   0 |   *   *   * 960  * |  0   1  1
. . x3o3x4o    96 |   96  192 |    0   32   96   64  48 |   0   0    0  16   24   8 |   *   *   *   * 60 |  0   0  2
------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x3o3x .    60 |  180   60 |  120   60   90   20   0 |  30  30   60  15    0   0 |   6  15   6   0  0 | 64   *  *
o3o3x . x4o    16 |   24   16 |   16    0   24    0   4 |   4   0   16   0    6   0 |   0   4   0   4  0 |  * 240  *
. o3x3o3x4o   480 |  960  960 |  320  320  960  320 240 |   0  80  320 160  240  40 |   0   0  32  80 10 |  *   * 12

o3o3x3o3x4/3o

. . . . .   . | 1920 |    6    4 |    6    3   12    2   2 |   2   3   12   6    6   1 |   1   4   6   6  3 |  2   2  3
--------------+------+-----------+-------------------------+---------------------------+--------------------+----------
. . x . .   . |    2 | 5760    * |    2    1    2    0   0 |   1   2    4   2    1   0 |   1   2   4   2  1 |  2   1  2
. . . . x   . |    2 |    * 3840 |    0    0    3    1   1 |   0   0    3   3    3   1 |   0   1   3   3  3 |  1   1  3
--------------+------+-----------+-------------------------+---------------------------+--------------------+----------
. o3x . .   . |    3 |    3    0 | 3840    *    *    *   * |   1   1    2   0    0   0 |   1   2   2   1  0 |  2   1  1
. . x3o .   . |    3 |    3    0 |    * 1920    *    *   * |   0   2    0   2    0   0 |   1   0   4   0  1 |  2   0  2
. . x . x   . |    4 |    2    2 |    *    * 5760    *   * |   0   0    2   1    1   0 |   0   1   2   2  1 |  1   1  2
. . . o3x   . |    3 |    0    3 |    *    *    * 1280   * |   0   0    0   3    0   1 |   0   0   3   0  3 |  1   0  3
. . . . x4/3o |    4 |    0    4 |    *    *    *    * 960 |   0   0    0   0    3   1 |   0   0   0   3  3 |  0   1  3
--------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x . .   .     4 |    6    0 |    4    0    0    0   0 | 960   *    *   *    *   * |   1   2   0   0  0 |  2   1  0
. o3x3o .   .     6 |   12    0 |    4    4    0    0   0 |   * 960    *   *    *   * |   1   0   2   0  0 |  2   0  1
. o3x . x   .     6 |    6    3 |    2    0    3    0   0 |   *   * 3840   *    *   * |   0   1   1   1  0 |  1   1  1
. . x3o3x   .    12 |   12   12 |    0    4    6    4   0 |   *   *    * 960    *   * |   0   0   2   0  1 |  1   0  2
. . x . x4/3o     8 |    4    8 |    0    0    4    0   2 |   *   *    *   * 1440   * |   0   0   0   2  1 |  0   1  2
. . . o3x4/3o    12 |    0   24 |    0    0    0    8   6 |   *   *    *   *    * 160 |   0   0   0   0  3 |  0   0  3
--------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x3o .   .    10 |   30    0 |   20   10    0    0   0 |   5   5    0   0    0   0 | 192   *   *   *  * |  2   0  0
o3o3x . x   .     8 |   12    4 |    8    0    6    0   0 |   2   0    4   0    0   0 |   * 960   *   *  * |  1   1  0
. o3x3o3x   .    30 |   60   30 |   20   20   30   10   0 |   0   5   10   5    0   0 |   *   * 384   *  * |  1   0  1
. o3x . x4/3o    12 |   12   12 |    4    0   12    0   3 |   0   0    4   0    3   0 |   *   *   * 960  * |  0   1  1
. . x3o3x4/3o    96 |   96  192 |    0   32   96   64  48 |   0   0    0  16   24   8 |   *   *   *   * 60 |  0   0  2
--------------+------+-----------+-------------------------+---------------------------+--------------------+----------
o3o3x3o3x   .    60 |  180   60 |  120   60   90   20   0 |  30  30   60  15    0   0 |   6  15   6   0  0 | 64   *  *
o3o3x . x4/3o    16 |   24   16 |   16    0   24    0   4 |   4   0   16   0    6   0 |   0   4   0   4  0 |  * 240  *
. o3x3o3x4/3o   480 |  960  960 |  320  320  960  320 240 |   0  80  320 160  240  40 |   0   0  32  80 10 |  *   * 12

x3o3x *b3x3o3o

. . .    . . . | 1920 |    2    2    6 |   1   2    6   1    3    6    6 |   1   3    6    6   3   3    6   2 |  3   3   6   2   3   1   2 |  3  1   2  1
---------------+------+----------------+---------------------------------+------------------------------------+----------------------------+-------------
x . .    . . . |    2 | 1920    *    * |   1   1    3   0    0    0    0 |   1   3    3    3   0   0    0   0 |  3   3   3   1   0   0   0 |  3  1   1  0
. . x    . . . |    2 |    * 1920    * |   0   1    0   1    0    3    0 |   1   0    3    0   3   0    3   0 |  3   0   3   0   3   0   1 |  3  0   1  1
. . .    x . . |    2 |    *    * 5760 |   0   0    1   0    1    1    2 |   0   1    1    2   1   2    2   1 |  1   2   2   1   2   1   1 |  2  1   1  1
---------------+------+----------------+---------------------------------+------------------------------------+----------------------------+-------------
x3o .    . . . |    3 |    3    0    0 | 640   *    *   *    *    *    * |   1   3    0    0   0   0    0   0 |  3   3   0   0   0   0   0 |  3  1   0  0
x . x    . . . |    4 |    2    2    0 |   * 960    *   *    *    *    * |   1   0    3    0   0   0    0   0 |  3   0   3   0   0   0   0 |  3  0   1  0
x . .    x . . |    4 |    2    0    2 |   *   * 2880   *    *    *    * |   0   1    1    2   0   0    0   0 |  1   2   2   1   0   0   0 |  2  1   1  0
. o3x    . . . |    3 |    0    3    0 |   *   *    * 640    *    *    * |   1   0    0    0   3   0    0   0 |  3   0   0   0   3   0   0 |  3  0   0  1
. o . *b3x . . |    3 |    0    0    3 |   *   *    *   * 1920    *    * |   0   1    0    0   1   2    0   0 |  1   2   0   0   2   1   0 |  2  1   0  1
. . x    x . . |    4 |    0    2    2 |   *   *    *   *    * 2880    * |   0   0    1    0   1   0    2   0 |  1   0   2   0   2   0   1 |  2  0   1  1
. . .    x3o . |    3 |    0    0    3 |   *   *    *   *    *    * 3840 |   0   0    0    1   0   1    1   1 |  0   1   1   1   1   1   1 |  1  1   1  1
---------------+------+----------------+---------------------------------+------------------------------------+----------------------------+-------------
x3o3x    . . .    12 |   12   12    0 |   4   6    0   4    0    0    0 | 160   *    *    *   *   *    *   * |  3   0   0   0   0   0   0 |  3  0   0  0
x3o . *b3x . .    12 |   12    0   12 |   4   0    6   0    4    0    0 |   * 480    *    *   *   *    *   * |  1   2   0   0   0   0   0 |  2  1   0  0
x . x    x . .     8 |    4    4    4 |   0   2    2   0    0    2    0 |   *   * 1440    *   *   *    *   * |  1   0   2   0   0   0   0 |  2  0   1  0
x . .    x3o .     6 |    3    0    6 |   0   0    3   0    0    0    2 |   *   *    * 1920   *   *    *   * |  0   1   1   1   0   0   0 |  1  1   1  0
. o3x *b3x . .    12 |    0   12   12 |   0   0    0   4    4    6    0 |   *   *    *    * 480   *    *   * |  1   0   0   0   2   0   0 |  2  0   0  1
. o . *b3x3o .     6 |    0    0   12 |   0   0    0   0    4    0    4 |   *   *    *    *   * 960    *   * |  0   1   0   0   1   1   0 |  1  1   0  1
. . x    x3o .     6 |    0    3    6 |   0   0    0   0    0    3    2 |   *   *    *    *   *   * 1920   * |  0   0   1   0   1   0   1 |  1  0   1  1
. . .    x3o3o     4 |    0    0    6 |   0   0    0   0    0    0    4 |   *   *    *    *   *   *    * 960 |  0   0   0   1   0   1   1 |  0  1   1  1
---------------+------+----------------+---------------------------------+------------------------------------+----------------------------+-------------
x3o3x *b3x . .    96 |   96   96   96 |  32  48   48  32   32   48    0 |   8   8   24    0   8   0    0   0 | 60   *   *   *   *   *   * |  2  0   0  0
x3o . *b3x3o .    30 |   30    0   60 |  10   0   30   0   20    0   20 |   0   5    0   10   0   5    0   0 |  * 192   *   *   *   *   * |  1  1   0  0
x . x    x3o .    12 |    6    6   12 |   0   3    6   0    0    6    4 |   0   0    3    2   0   0    2   0 |  *   * 960   *   *   *   * |  1  0   1  0
x . .    x3o3o     8 |    4    0   12 |   0   0    6   0    0    0    8 |   0   0    0    4   0   0    0   2 |  *   *   * 480   *   *   * |  0  1   1  0
. o3x *b3x3o .    30 |    0   30   60 |   0   0    0  10   20   30   20 |   0   0    0    0   5   5   10   0 |  *   *   *   * 192   *   * |  1  0   0  1
. o . *b3x3o3o    10 |    0    0   30 |   0   0    0   0   10    0   20 |   0   0    0    0   0   5    0   5 |  *   *   *   *   * 192   * |  0  1   0  1
. . x    x3o3o     8 |    0    4   12 |   0   0    0   0    0    6    8 |   0   0    0    0   0   0    4   2 |  *   *   *   *   *   * 480 |  0  0   1  1
---------------+------+----------------+---------------------------------+------------------------------------+----------------------------+-------------
x3o3x *b3x3o .   480 |  480  480  960 | 160 240  480 160  320  480  320 |  40  80  240  160  80  80  160   0 | 10  16  80   0  16   0   0 | 12  *   *  *
x3o . *b3x3o3o    60 |   60    0  180 |  20   0   90   0   60    0  120 |   0  15    0   60   0  30    0  30 |  0   6   0  15   0   6   0 |  * 32   *  *
x . x    x3o3o    16 |    8    8   24 |   0   4   12   0    0   12   16 |   0   0    6    8   0   0    8   4 |  0   0   4   2   0   0   2 |  *  * 240  *
. o3x *b3x3o3o    60 |    0   60  180 |   0   0    0  20   60   90  120 |   0   0    0    0  15  30   60  30 |  0   0   0   0   6   6  15 |  *  *   * 32

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