Acronym sarz
Name small rhombated hecatonicosoctaexon,
cantellated heptacross
Circumradius sqrt(3) = 1.732051
Coordinates (2/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3o3x3o3o3o4o

. . . . . . . | 840 |   2   16 |   1   16    8    48 |   8   48   24    64 |  24   64   32   32 |  32   32  16   2 |  16  2  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x . . . . . . |   2 | 840    * |   1    8    0     0 |   8   24    0     0 |  24   32    0    0 |  32   16   0   0 |  16  1  0
. . x . . . . |   2 |   * 6720 |   0    1    1     6 |   1    6    6    12 |   6   12   12    8 |  12    8   8   1 |   8  1  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x3o . . . . . |   3 |   3    0 | 280    *    *     *    8    0    0     0 |  24    0    0    0 |  32    0   0   0 |  16  0  0
x . x . . . . |   4 |   2    2 |   * 3360    *     * |   1    6    0     0 |   6   12    0    0 |  12    8   0   0 |   8  1  0
. o3x . . . . |   3 |   0    3 |   *    * 2240     * |   1    0    6     0 |   6    0   12    0 |  12    0   8   0 |   8  0  1
. . x3o . . . |   3 |   0    3 |   *    *    * 13440 |   0    1    1     4 |   1    4    4    4 |   4    4   4   1 |   4  1  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x3o3x . . . .   12 |  12   12 |   4    6    4     0 | 560    *    *     *    6    0    0    0 |  12    0   0   0 |   8  0  0
x . x3o . . .    6 |   3    6 |   0    3    0     2 |   * 6720    *     * |   1    4    0    0 |   4    4   0   0 |   4  1  0
. o3x3o . . .    6 |   0   12 |   0    0    4     4 |   *    * 3360     * |   1    0    4    0 |   4    0   4   0 |   4  0  1
. . x3o3o . .    4 |   0    6 |   0    0    0     4 |   *    *    * 13440 |   0    1    1    2 |   1    2   2   1 |   2  1  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x3o3x3o . . .   30 |  30   60 |  10   30   20    20 |   5   10    5     0 | 672    *    *    * |   4    0   0   0 |   4  0  0
x . x3o3o . .    8 |   4   12 |   0    6    0     8 |   0    4    0     2 |   * 6720    *    * |   1    2   0   0 |   2  1  0
. o3x3o3o . .   10 |   0   30 |   0    0   10    20 |   0    0    5     5 |   *    * 2688    * |   1    0   2   0 |   2  0  1
. . x3o3o3o .    5 |   0   10 |   0    0    0    10 |   0    0    0     5 |   *    *    * 5376 |   0    1   1   1 |   1  1  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x3o3x3o3o . .   60 |  60  180 |  20   90   60   120 |  15   60   30    30 |   6   15    6    0 | 448    *   *   * |   2  0  0
x . x3o3o3o .   10 |   5   20 |   0   10    0    20 |   0   10    0    10 |   0    5    0    2 |   * 2688   *   * |   1  1  0
. o3x3o3o3o .   15 |   0   60 |   0    0   20    60 |   0    0   15    30 |   0    0    6    6 |   *    * 896   * |   1  0  1
. . x3o3o3o4o   10 |   0   40 |   0    0    0    80 |   0    0    0    80 |   0    0    0   32 |   *    *   * 168 |   0  1  1
--------------+-----+----------+---------------------+---------------------+--------------------+------------------+----------
x3o3x3o3o3o .  105 | 105  420 |  35  210  140   420 |  35  210  105   210 |  21  105   42   42 |   7   21   7   0 | 128  *  *
x . x3o3o3o4o   20 |  10   80 |   0   40    0   160 |   0   80    0   160 |   0   80    0   64 |   0   32   0   2 |   * 84  *
. o3x3o3o3o4o   60 |   0  480 |   0    0  160   960 |   0    0  240   960 |   0    0  192  384 |   0    0  64  12 |   *  * 14

o3o3o *b3o3x3o3x

. . .    . . . . | 840 |   16   2 |    48    8   16   1 |    64   24   48   8 |   16   16   32   64  24 |   2   8   16   8   16  32 |  1  2  8  8
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
. . .    . x . . |   2 | 6720   * |     6    1    1   0 |    12    6    6   1 |    4    4   12   12   6 |   1   4    4   4    4  12 |  1  1  4  4
. . .    . . . x |   2 |    * 840 |     0    0    8   1 |     0    0   24   8 |    0    0    0   32  24 |   0   0    8   0    8  32 |  0  1  8  8
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
. . .    o3x . . |   3 |    3   0 | 13440    *    *   * |     4    1    1   0 |    2    2    4    4   1 |   1   2    2   2    2   4 |  1  1  2  2
. . .    . x3o . |   3 |    3   0 |     * 2240    *   * |     0    6    0   1 |    0    0   12    0   6 |   0   4    0   4    0  12 |  1  0  4  4
. . .    . x . x |   4 |    2   2 |     *    * 3360   * |     0    0    6   1 |    0    0    0   12   6 |   0   0    4   0    4  12 |  0  1  4  4
. . .    . . o3x |   3 |    0   3 |     *    *    * 280      0    0    0   8 |    0    0    0    0  24 |   0   0    0   0    0  32 |  0  0  8  8
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
. o . *b3o3x . .    4 |    6   0 |     4    0    0   0 | 13440    *    *   * |    1    1    1    1   0 |   1   1    1   1    1   1 |  1  1  1  1
. . .    o3x3o .    6 |   12   0 |     4    4    0   0 |     * 3360    *   * |    0    0    4    0   1 |   0   2    0   2    0   4 |  1  0  2  2
. . .    o3x . x    6 |    6   3 |     2    0    3   0 |     *    * 6720   * |    0    0    0    4   1 |   0   0    2   0    2   4 |  0  1  2  2
. . .    . x3o3x   12 |   12  12 |     0    4    6   4 |     *    *    * 560     0    0    0    0   6 |   0   0    0   0    0  12 |  0  0  4  4
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
o3o . *b3o3x . .    5 |   10   0 |    10    0    0   0 |     5    0    0   0 | 2688    *    *    *   * |   1   1    1   0    0   0 |  1  1  1  0
. o3o *b3o3x . .    5 |   10   0 |    10    0    0   0 |     5    0    0   0 |    * 2688    *    *   * |   1   0    0   1    1   0 |  1  1  0  1
. o . *b3o3x3o .   10 |   30   0 |    20   10    0   0 |     5    5    0   0 |    *    * 2688    *   * |   0   1    0   1    0   1 |  1  0  1  1
. o . *b3o3x . x    8 |   12   4 |     8    0    6   0 |     2    0    4   0 |    *    *    * 6720   * |   0   0    1   0    1   1 |  0  1  1  1
. . .    o3x3o3x   30 |   60  30 |    20   20   30  10 |     0    5   10   5 |    *    *    *    * 672 |   0   0    0   0    0   4 |  0  0  2  2
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
o3o3o *b3o3x . .   10 |   40   0 |    80    0    0   0 |    80    0    0   0 |   16   16    0    0   0 | 168   *    *   *    *   * |  1  1  0  0
o3o . *b3o3x3o .   15 |   60   0 |    60   20    0   0 |    30   15    0   0 |    6    0    6    0   0 |   * 448    *   *    *   * |  1  0  1  0
o3o . *b3o3x . x   10 |   20   5 |    20    0   10   0 |    10    0   10   0 |    2    0    0    5   0 |   *   * 1344   *    *   * |  0  1  1  0
. o3o *b3o3x3o .   15 |   60   0 |    60   20    0   0 |    30   15    0   0 |    0    6    6    0   0 |   *   *    * 448    *   * |  1  0  0  1
. o3o *b3o3x . x   10 |   20   5 |    20    0   10   0 |    10    0   10   0 |    0    2    0    5   0 |   *   *    *   * 1344   * |  0  1  0  1
. o . *b3o3x3o3x   60 |  180  60 |   120   60   90  20 |    30   30   60  15 |    0    0    6   15   6 |   *   *    *   *    * 448 |  0  0  1  1
-----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------
o3o3o *b3o3x3o .   60 |  480   0 |   960  160    0   0 |   960  240    0   0 |  192  192  192    0   0 |  12  32    0  32    0   0 | 14  *  *  *
o3o3o *b3o3x . x   20 |   80  10 |   160    0   40   0 |   160    0   80   0 |   32   32    0   80   0 |   2   0   16   0   16   0 |  * 84  *  *
o3o . *b3o3x3o3x  105 |  420 105 |   420  140  210  35 |   210  105  210  35 |   42    0   42  105  21 |   0   7   21   0    0   7 |  *  * 64  *
. o3o *b3o3x3o3x  105 |  420 105 |   420  140  210  35 |   210  105  210  35 |    0   42   42  105  21 |   0   0    0   7   21   7 |  *  *  * 64

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