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
Face vector	320, 1280, 1280, 440, 52
Confer	general polytopal classes: Wythoffian polytera
External links

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