Acronym rawcbinant (old: recarnit)
Name retrosphenary cellibiprismatopenteractipenteractitriacontaditeron,
retrocellirhombated penteractitriacontaditeron
Circumradius sqrt[17+8 sqrt(2)]/2 = 2.660531
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army carnit
Colonel of regiment carnit

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


Incidence matrix according to Dynkin symbol

x3o3x3o4/3x4*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*c |   8 |   0    4   4 |   *   *   *   *   * 480   * |   0   0   0   1   0   0  1  1 |  0  1  0  1  1
. . . o4/3x    |   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*c   16 |   8    8   8 |   0   4   4   0   0   2   0 |   *   *   * 240   *   *  *  * |  0  1  0  1  0
x . . o4/3x       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*c   24 |   0   24  12 |   0   0   0   8   0   6   0 |   *   *   *   *   *   * 80  * |  0  1  0  0  1
. . x3o4/3x4*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*c  192 | 192  192  96 |  64  96  96  64   0  48   0 |  16  32   0  24   0   0  8  0 |  * 10  *  *  *
x3o . o4/3x      12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0  0  0 |  *  * 80  *  *
x . x3o4/3x4*c   48 |  24   48  48 |   0  24  24   0  16  12  12 |   0   0   8   6   6   0  0  2 |  *  *  * 40  *
. o3x3o4/3x4*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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