Acronym rawvax
Name retrosphenary hexeract
Circumradius sqrt[(7+4 sqrt(2))/2] = 2.515637
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army srox
Colonel of regiment srox
Face vector 960, 4800, 6320, 3520, 948, 88
Confer
general polytopal classes:
Wythoffian polypeta  

As abstract polytope rawn is isomorphic to wavinant, thereby replacing octagons by octagrams, resp. tic by quith and socco by gocco, resp. tat by quitit and rawvatoth by wavitoth, resp. tan by quittin and rawn by wavinant. – As such rawvax is a lieutenant.


Incidence matrix according to Dynkin symbol

o3o3o3x3o4/3x4*d

. . . . .   .    | 960 |    8   2 |   12    4   8   1 |    8   6  12   4 |   2   4   8  6 |  1  2  4
-----------------+-----+----------+-------------------+------------------+----------------+---------
. . . x .   .    |   2 | 3840   * |    3    1   1   0 |    3   3   3   1 |   1   3   3  3 |  1  1  3
. . . . .   x    |   2 |    * 960 |    0    0   4   1 |    0   0   6   4 |   0   0   4  6 |  0  1  4
-----------------+-----+----------+-------------------+------------------+----------------+---------
. . o3x .   .    |   3 |    3   0 | 3840    *   *   * |    2   1   1   0 |   1   2   2  1 |  1  1  2
. . . x3o   .    |   3 |    3   0 |    * 1280   *   * |    0   3   0   1 |   0   3   0  3 |  1  0  3
. . . x .   x4*d |   8 |    4   4 |    *    * 960   * |    0   0   3   1 |   0   0   3  3 |  0  1  3
. . . . o4/3x    |   4 |    0   4 |    *    *   * 240     0   0   0   4 |   0   0   0  6 |  0  0  4
-----------------+-----+----------+-------------------+------------------+----------------+---------
. o3o3x .   .       4 |    6   0 |    4    0   0   0 | 1920   *   *   * |   1   1   1  0 |  1  1  1
. . o3x3o   .       6 |   12   0 |    4    4   0   0 |    * 960   *   * |   0   2   0  1 |  1  0  2
. . o3x .   x4*d   24 |   24  12 |    8    0   6   0 |    *   * 480   * |   0   0   2  1 |  0  1  2
. . . x3o4/3x4*d   24 |   24  24 |    0    8   6   6 |    *   *   * 160 |   0   0   0  3 |  0  0  3
-----------------+-----+----------+-------------------+------------------+----------------+---------
o3o3o3x .   .       5 |   10   0 |   10    0   0   0 |    5   0   0   0 | 384   *   *  * |  1  1  0
. o3o3x3o   .      10 |   30   0 |   20   10   0   0 |    5   5   0   0 |   * 384   *  * |  1  0  1
. o3o3x .   x4*d   64 |   96  32 |   64    0  24   0 |   16   0   8   0 |   *   * 120  * |  0  1  1
. . o3x3o4/3x4*d   96 |  192  96 |   64   64  48  24 |    0  16   8   8 |   *   *   * 60 |  0  0  2
-----------------+-----+----------+-------------------+------------------+----------------+---------
o3o3o3x3o   .      15 |   60   0 |   60   20   0   0 |   30  15   0   0 |   6   6   0  0 | 64  *  *
o3o3o3x .   x4*d  160 |  320  80 |  320    0  80   0 |  160   0  40   0 |  32   0  10  0 |  * 12  *
. o3o3x3o4/3x4*d  320 |  960 320 |  640  320 240  80 |  160 160  80  40 |   0  32  10 10 |  *  * 12

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