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
```