Acronym sidacadint
Name small discellidispenteractitriacontaditeron
Circumradius sqrt[17+4 sqrt(2)]/2 = 2.379961
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment sibacadint
Face vector 1920, 6720, 6720, 2160, 132
Confer
general polytopal classes:
Wythoffian polytera  

As abstract polytope sidacadint is isomorphic to gidacadint, thereby replacing octagons by octagrams, resp. replacing the querco by sirco, op by stop, socco by gocco, and girco by quitco, resp. replacing the gikviphado by skiviphado, quercope by sircope, gircope by quitcope, and sichado by gichado. As such sidacadint is a lieutenant.


Incidence matrix according to Dynkin symbol

x3o3x3x *b4/3x4*c

. . . .      .    | 1920 |    2    2   1    2 |   1   2   2   2   1   1   2   2   2 |   1   1  1   2   2   2   1  1   1  2 |  1  1  1  2  1
------------------+------+--------------------+-------------------------------------+--------------------------------------+---------------
x . . .      .    |    2 | 1920    *   *    * |   1   1   1   1   0   0   0   0   0 |   1   1  1   1   1   1   0  0   0  0 |  1  1  1  1  0
. . x .      .    |    2 |    * 1920   *    * |   0   1   0   0   1   0   1   1   0 |   1   0  0   1   1   0   1  1   0  1 |  1  1  0  1  1
. . . x      .    |    2 |    *    * 960    * |   0   0   2   0   0   0   2   0   2 |   0   1  0   2   0   2   1  0   1  2 |  1  0  1  2  1
. . . .      x    |    2 |    *    *   * 1920 |   0   0   0   1   0   1   0   1   1 |   0   0  1   0   1   1   0  1   1  1 |  0  1  1  1  1
------------------+------+--------------------+-------------------------------------+--------------------------------------+---------------
x3o . .      .    |    3 |    3    0   0    0 | 640   *   *   *   *   *   *   *   * |   1   1  1   0   0   0   0  0   0  0 |  1  1  1  0  0
x . x .      .    |    4 |    2    2   0    0 |   * 960   *   *   *   *   *   *   * |   1   0  0   1   1   0   0  0   0  0 |  1  1  0  1  0
x . . x      .    |    4 |    2    0   2    0 |   *   * 960   *   *   *   *   *   * |   0   1  0   1   0   1   0  0   0  0 |  1  0  1  1  0
x . . .      x    |    4 |    2    0   0    2 |   *   *   * 960   *   *   *   *   * |   0   0  1   0   1   1   0  0   0  0 |  0  1  1  1  0
. o3x .      .    |    3 |    0    3   0    0 |   *   *   *   * 640   *   *   *   * |   1   0  0   0   0   0   1  1   0  0 |  1  1  0  0  1
. o . . *b4/3x    |    4 |    0    0   0    4 |   *   *   *   *   * 480   *   *   * |   0   0  1   0   0   0   0  1   1  0 |  0  1  1  0  1
. . x3x      .    |    6 |    0    3   3    0 |   *   *   *   *   *   * 640   *   * |   0   0  0   1   0   0   1  0   0  1 |  1  0  0  1  1
. . x .      x4*c |    8 |    0    4   0    4 |   *   *   *   *   *   *   * 480   * |   0   0  0   0   1   0   0  1   0  1 |  0  1  0  1  1  {8}
. . . x      x    |    4 |    0    0   2    2 |   *   *   *   *   *   *   *   * 960 |   0   0  0   0   0   1   0  0   1  1 |  0  0  1  1  1
------------------+------+--------------------+-------------------------------------+--------------------------------------+---------------
x3o3x .      .       12 |   12   12   0    0 |   4   6   0   0   4   0   0   0   0 | 160   *  *   *   *   *   *  *   *  * |  1  1  0  0  0
x3o . x      .        6 |    6    0   3    0 |   2   0   3   0   0   0   0   0   0 |   * 320  *   *   *   *   *  *   *  * |  1  0  1  0  0
x3o . . *b4/3x       24 |   24    0   0   24 |   8   0   0  12   0   6   0   0   0 |   *   * 80   *   *   *   *  *   *  * |  0  1  1  0  0
x . x3x      .       12 |    6    6   6    0 |   0   3   3   0   0   0   2   0   0 |   *   *  * 320   *   *   *  *   *  * |  1  0  0  1  0
x . x .      x4*c    16 |    8    8   0    8 |   0   4   0   4   0   0   0   2   0 |   *   *  *   * 240   *   *  *   *  * |  0  1  0  1  0
x . . x      x        8 |    4    0   4    4 |   0   0   2   2   0   0   0   0   2 |   *   *  *   *   * 480   *  *   *  * |  0  0  1  1  0
. o3x3x      .       12 |    0   12   6    0 |   0   0   0   0   4   0   4   0   0 |   *   *  *   *   *   * 160  *   *  * |  1  0  0  0  1
. o3x . *b4/3x4*c    24 |    0   24   0   24 |   0   0   0   0   8   6   0   6   0 |   *   *  *   *   *   *   * 80   *  * |  0  1  0  0  1
. o . x *b4/3x        8 |    0    0   4    8 |   0   0   0   0   0   2   0   0   4 |   *   *  *   *   *   *   *  * 240  * |  0  0  1  0  1
. . x3x      x4*c    48 |    0   24  24   24 |   0   0   0   0   0   0   8   6  12 |   *   *  *   *   *   *   *  *   * 80 |  0  0  0  1  1
------------------+------+--------------------+-------------------------------------+--------------------------------------+---------------
x3o3x3x      .       60 |   60   60  30    0 |  20  30  30   0  20   0  20   0   0 |   5  10  0  10   0   0   5  0   0  0 | 32  *  *  *  *
x3o3x . *b4/3x4*c   192 |  192  192   0  192 |  64  96   0  96  64  48   0  48   0 |  16   0  8   0  24   0   0  8   0  0 |  * 10  *  *  *
x3o . x *b4/3x       48 |   48    0  24   48 |  16   0  24  24   0  12   0   0  24 |   0   8  2   0   0  12   0  0   6  0 |  *  * 40  *  *
x . x3x      x4*c    96 |   48   48  48   48 |   0  24  24  24   0   0  16  12  24 |   0   0  0   8   6  12   0  0   0  2 |  *  *  * 40  *
. o3x3x *b4/3x4*c   192 |    0  192  96  192 |   0   0   0   0  64  48  64  48  96 |   0   0  0   0   0   0  16  8  24  8 |  *  *  *  * 10

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