Acronym wacbinant
Name sphenary cellibiprismatopenteractipenteractitriacontaditeron
Field of sections
 ©
Circumradius sqrt[17-8 sqrt(2)]/2 = 1.192297
Vertex figure
 ©
Coordinates ((2 sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: gaqript garpop gichado giphado girpith goccope grohp quiproh quitcope rawvtip srip tisdip wavitoth
gadencorn 103200100400400000
garcornit 001010000003208010
wacbinant 000004001000328010
& others)

As abstract polytope wacbinant is isomorphic to recarnit, thereby replacing octagrams by octagons, resp. gocco by socco, stop by op, and quith by tic, resp. quiproh by proh, goccope by soccope, and wavitoth by rawvatoth.


Incidence matrix according to Dynkin symbol

x3o3x3o4x4/3*c

. . . . .      | 960 |   2    4   2 |   1   4   4   2   2   4   1 |   2   2   2   4   2   1  2  2 |  1  2  1  2  1
---------------+-----+--------------+-----------------------------+-------------------------------+---------------
x . . . .      |   2 | 960    *   * |   1   2   2   0   0   0   0 |   2   2   1   2   1   0  0  0 |  1  2  1  1  0
. . x . .      |   2 |   * 1920   * |   0   1   0   1   1   1   0 |   1   0   1   1   0   1  1  1 |  1  1  0  1  1
. . . . x      |   2 |   *    * 960 |   0   0   2   0   0   2   1 |   0   1   0   2   2   0  1  2 |  0  1  1  2  1
---------------+-----+--------------+-----------------------------+-------------------------------+---------------
x3o . . .      |   3 |   3    0   0 | 320   *   *   *   *   *   * |   2   2   0   0   0   0  0  0 |  1  2  1  0  0
x . x . .      |   4 |   2    2   0 |   * 960   *   *   *   *   * |   1   0   1   1   0   0  0  0 |  1  1  0  1  0
x . . . x      |   4 |   2    0   2 |   *   * 960   *   *   *   * |   0   1   0   1   1   0  0  0 |  0  1  1  1  0
. o3x . .      |   3 |   0    3   0 |   *   *   * 640   *   *   * |   1   0   0   0   0   1  1  0 |  1  1  0  0  1
. . x3o .      |   3 |   0    3   0 |   *   *   *   * 640   *   * |   0   0   1   0   0   1  0  1 |  1  0  0  1  1
. . x . x4/3*c |   8 |   0    4   4 |   *   *   *   *   * 480   * |   0   0   0   1   0   0  1  1 |  0  1  0  1  1
. . . o4x      |   4 |   0    0   4 |   *   *   *   *   *   * 240 |   0   0   0   0   2   0  0  2 |  0  0  1  2  1
---------------+-----+--------------+-----------------------------+-------------------------------+---------------
x3o3x . .        12 |  12   12   0 |   4   6   0   4   0   0   0 | 160   *   *   *   *   *  *  * |  1  1  0  0  0
x3o . . x         6 |   6    0   3 |   2   0   3   0   0   0   0 |   * 320   *   *   *   *  *  * |  0  1  1  0  0
x . x3o .         6 |   3    6   0 |   0   3   0   0   2   0   0 |   *   * 320   *   *   *  *  * |  1  0  0  1  0
x . x . x4/3*c   16 |   8    8   8 |   0   4   4   0   0   2   0 |   *   *   * 240   *   *  *  * |  0  1  0  1  0
x . . o4x         8 |   4    0   8 |   0   0   4   0   0   0   2 |   *   *   *   * 240   *  *  * |  0  0  1  1  0
. o3x3o .         6 |   0   12   0 |   0   0   0   4   4   0   0 |   *   *   *   *   * 160  *  * |  1  0  0  0  1
. o3x . x4/3*c   24 |   0   24  12 |   0   0   0   8   0   6   0 |   *   *   *   *   *   * 80  * |  0  1  0  0  1
. . x3o4x4/3*c   24 |   0   24  24 |   0   0   0   0   8   6   6 |   *   *   *   *   *   *  * 80 |  0  0  0  1  1
---------------+-----+--------------+-----------------------------+-------------------------------+---------------
x3o3x3o .        30 |  30   60   0 |  10  30   0  20  20   0   0 |   5   0  10   0   0   5  0  0 | 32  *  *  *  *
x3o3x . x4/3*c  192 | 192  192  96 |  64  96  96  64   0  48   0 |  16  32   0  24   0   0  8  0 |  * 10  *  *  *
x3o . o4x        12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0  0  0 |  *  * 80  *  *
x . x3o4x4/3*c   48 |  24   48  48 |   0  24  24   0  16  12  12 |   0   0   8   6   6   0  0  2 |  *  *  * 40  *
. o3x3o4x4/3*c   96 |   0  192  96 |   0   0   0  64  64  48  24 |   0   0   0   0   0  16  8  8 |  *  *  *  * 10

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