Acronym rawn (old: rawvanant)
Name retrosphenary penteract
Circumradius sqrt[11+6 sqrt(2)]/2 = 2.207107
Coordinates ((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 sirn
Colonel of regiment sirn

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. – As such rawn is a lieutenant.


Incidence matrix according to Dynkin symbol

o3o3x3o4/3x4*c

. . . .   .    | 320 |   6   2 |   6   3   6  1 |   2   3  6  3 |  1  2  3
---------------+-----+---------+----------------+---------------+---------
. . x .   .    |   2 | 960   * |   2   1   1  0 |   1   2  2  1 |  1  1  2
. . . .   x    |   2 |   * 320 |   0   0   3  1 |   0   0  3  3 |  0  1  3
---------------+-----+---------+----------------+---------------+---------
. o3x .   .    |   3 |   3   0 | 640   *   *  * |   1   1  1  0 |  1  1  1
. . x3o   .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
. . x .   x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
. . . o4/3x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
---------------+-----+---------+----------------+---------------+---------
o3o3x .   .       4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
. o3x3o   .       6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
. o3x .   x4*c   24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
. . x3o4/3x4*c   24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
---------------+-----+---------+----------------+---------------+---------
o3o3x3o   .      10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3o3x .   x4*c   64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
. o3x3o4/3x4*c   96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10

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