Acronym sirpin
Name small retroprismated penteract
Circumradius sqrt(2)+1/2 = 1.914214
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army span
Colonel of regiment span

As abstract polytope sirpin is isomorphic to fawdint, thereby replacing octagons by octagrams, resp. tic by quith and socco by gocco, resp. steth by gittith and rawvatoth by wavitoth. – As such sirpin is a lieutenant.


Incidence matrix according to Dynkin symbol

o3x3o3o *b4x4/3*c

. . . .    .      | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
------------------+-----+---------+-----------------+------------------+---------
. x . .    .      |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
. . . .    x      |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
------------------+-----+---------+-----------------+------------------+---------
o3x . .    .      |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
. x3o .    .      |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
. x . . *b4x      |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
. . o .    x4/3*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
------------------+-----+---------+-----------------+------------------+---------
o3x3o .    .         6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3x . . *b4x        24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
. x3o3o    .         4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
. x3o . *b4x4/3*c   24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
. . o3o    x4/3*c    8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
------------------+-----+---------+-----------------+------------------+---------
o3x3o3o    .        10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3x3o . *b4x4/3*c   96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
. x3o3o *b4x4/3*c   64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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