Acronym soro
Name small rhombated octeract,
cantellated octeract
Circumradius sqrt[5+3 sqrt(2)] = 3.040171
Inradius
wrt. hopip
sqrt[(121+84 sqrt(2))/28] = 2.926443
Inradius
wrt. roc
sqrt[17+12 sqrt(2)]/2 = 2.914214
Inradius
wrt. sersa
(1+sqrt(2))/2 = 1.207107
Dihedral angles
(at margins)
Face vector 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296
Confer
general polytopal classes:
Wythoffian polyzetta  
analogs:
rhombated hypercube rbCn  

As abstract polytope soro is isomorphic to qro, thereby replacing sirco by querco, srit by qrit, sirn by quarn, srox by qrax, and sersa by quersa.


Incidence matrix according to Dynkin symbol

o3o3o3o3o3x3o4x

o3o3o3o3o3o3o4o | 7168 |    12    2 |    30     6    12    1 |    40    15    30    6 |    30    20    40   15 |    12   15    30  20 |    2    6   12  15 |   1    2  6
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . . . x . . |    2 | 43008    * |     5     1     1    0 |    10     5     5    1 |    10    10    10    5 |     5   10    10  10 |    1    5    5  10 |   1    1  5
. . . . . . . x |    2 |     * 7168 |     0     0     6    1 |     0     0    15    6 |     0     0    20   15 |     0    0    15  20 |    0    0    6  15 |   0    1  6
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . . o3x . . |    3 |     3    0 | 71680     *     *    * |     4     1     1    0 |     6     4     4    1 |     4    6     6   4 |    1    4    4   6 |   1    1  4
. . . . . x3o . |    3 |     3    0 |     * 14336     *    * |     0     5     0    1 |     0    10     0    5 |     0   10     0  10 |    0    5    0  10 |   1    0  5
. . . . . x . x |    4 |     2    2 |     *     * 21504    * |     0     0     5    1 |     0     0    10    5 |     0    0    10  10 |    0    0    5  10 |   0    1  5
. . . . . . o4x |    4 |     0    4 |     *     *     * 1792 |     0     0     0    6 |     0     0     0   15 |     0    0     0  20 |    0    0    0  15 |   0    0  6
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . o3o3x . .     4 |     6    0 |     4     0     0    0 | 71680     *     *    * |     3     1     1    0 |     3    3     3   1 |    1    3    3   3 |   1    1  3
. . . . o3x3o .     6 |    12    0 |     4     4     0    0 |     * 17920     *    * |     0     4     0    1 |     0    6     0   4 |    0    4    0   6 |   1    0  4
. . . . o3x . x     6 |     6    3 |     2     0     3    0 |     *     * 35840    * |     0     0     4    1 |     0    0     6   4 |    0    0    4   6 |   0    1  4
. . . . . x3o4x    24 |    24   24 |     0     8    12    6 |     *     *     * 1792 |     0     0     0    5 |     0    0     0  10 |    0    0    0  10 |   0    0  5
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . o3o3o3x . .     5 |    10    0 |    10     0     0    0 |     5     0     0    0 | 43008     *     *    * |     2    1     1   0 |    1    2    2   1 |   1    1  2
. . . o3o3x3o .    10 |    30    0 |    20    10     0    0 |     5     5     0    0 |     * 14336     *    * |     0    3     0   1 |    0    3    0   3 |   1    0  3
. . . o3o3x . x     8 |    12    4 |     8     0     6    0 |     2     0     4    0 |     *     * 35840    * |     0    0     3   1 |    0    0    3   3 |   0    1  3
. . . . o3x3o4x    96 |   192   96 |    64    64    96   24 |     0    16    32    8 |     *     *     * 1120 |     0    0     0   4 |    0    0    0   6 |   0    0  4
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. o3o3o3o3x . .     6 |    15    0 |    20     0     0    0 |    15     0     0    0 |     6     0     0    0 | 14336    *     *   * |    1    1    1   0 |   1    1  1
. . o3o3o3x3o .    15 |    60    0 |    60    20     0    0 |    30    15     0    0 |     6     6     0    0 |     * 7168     *   * |    0    2    0   1 |   1    0  2
. . o3o3o3x . x    10 |    20    5 |    20     0    10    0 |    10     0    10    0 |     2     0     5    0 |     *    * 21504   * |    0    0    2   1 |   0    1  2
. . . o3o3x3o4x   320 |   960  320 |   640   320   480   80 |   160   160   320   40 |     0    32    80   10 |     *    *     * 448 |    0    0    0   3 |   0    0  3
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
o3o3o3o3o3x . .     7 |    21    0 |    35     0     0    0 |    35     0     0    0 |    21     0     0    0 |     7    0     0   0 | 2048    *    *   * |   1    1  0
. o3o3o3o3x3o .    21 |   105    0 |   140    35     0    0 |   105    35     0    0 |    42    21     0    0 |     7    7     0   0 |    * 2048    *   * |   1    0  1
. o3o3o3o3x . x    12 |    30    6 |    40     0    15    0 |    30     0    20    0 |    12     0    15    0 |     2    0     6   0 |    *    * 7168   * |   0    1  1
. . o3o3o3x3o4x   960 |  3840  960 |  3840  1280  1920  240 |  1920   960  1920  160 |   384   384   960   60 |     0   64   192  12 |    *    *    * 112 |   0    0  2
----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
o3o3o3o3o3x3o .    28 |   168    0 |   280    56     0    0 |   280    70     0    0 |   168    56     0    0 |    56   28     0   0 |    8    8    0   0 | 256    *  *
o3o3o3o3o3x . x    14 |    42    7 |    70     0    21    0 |    70     0    35    0 |    42     0    35    0 |    14    0    21   0 |    2    0    7   0 |   * 1024  *
. o3o3o3o3x3o4x  2688 | 13440 2688 | 17920  4480  6720  672 | 13440  4480  8960  560 |  5376  2688  6720  280 |   896  896  2688  84 |    0  128  448  14 |   *    * 16

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