Acronym	setitdin
Name	small tesseractitriacontidiadispenteract
Circumradius	sqrt[15+6 sqrt(2)]/2 = 2.423081
Coordinates	((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment	cappin
Face vector	640, 2240, 2160, 760, 92
Confer	general polytopal classes: Wythoffian polytera
External links

As abstract polytope setitdin is isomorphic to getitdin, thereby replacing octagons by octagrams, resp. girco by quitco and socco by gocco, resp. steth by gittith and sichado by gichado. – As such setitdin is a lieutenant.

Incidence matrix according to Dynkin symbol

x3x3o3o *b4x4/3*c

. . . .    .      | 640 |   1   3   3 |   3   3   3   3   3 |   3  3   3   1  3  1 |  1  3  1  1
------------------+-----+-------------+---------------------+----------------------+------------
x . . .    .      |   2 | 320   *   * |   3   3   0   0   0 |   3  3   3   0  0  0 |  1  3  1  0
. x . .    .      |   2 |   * 960   * |   1   0   2   1   0 |   2  1   0   1  2  0 |  1  2  0  1
. . . .    x      |   2 |   *   * 960 |   0   1   0   1   2 |   0  1   2   0  2  1 |  0  2  1  1
------------------+-----+-------------+---------------------+----------------------+------------
x3x . .    .      |   6 |   3   3   0 | 320   *   *   *   * |   2  1   0   0  0  0 |  1  2  0  0
x . . .    x      |   4 |   2   0   2 |   * 480   *   *   * |   0  1   2   0  0  0 |  0  2  1  0
. x3o .    .      |   3 |   0   3   0 |   *   * 640   *   * |   1  0   0   1  1  0 |  1  1  0  1
. x . . *b4x      |   8 |   0   4   4 |   *   *   * 240   * |   0  1   0   0  2  0 |  0  2  0  1
. . o .    x4/3*c |   4 |   0   0   4 |   *   *   *   * 480 |   0  0   1   0  1  1 |  0  1  1  1
------------------+-----+-------------+---------------------+----------------------+------------
x3x3o .    .      ♦  12 |   6  12   0 |   4   0   4   0   0 | 160  *   *   *  *  * |  1  1  0  0
x3x . . *b4x      ♦  48 |  24  24  24 |   8  12   0   6   0 |   * 40   *   *  *  * |  0  2  0  0
x . o .    x4/3*c ♦   8 |   4   0   8 |   0   4   0   0   2 |   *  * 240   *  *  * |  0  1  1  0
. x3o3o    .      ♦   4 |   0   6   0 |   0   0   4   0   0 |   *  *   * 160  *  * |  1  0  0  1
. x3o . *b4x4/3*c ♦  24 |   0  24  24 |   0   0   8   6   6 |   *  *   *   * 80  * |  0  1  0  1
. . o3o    x4/3*c ♦   8 |   0   0  12 |   0   0   0   0   6 |   *  *   *   *  * 80 |  0  0  1  1
------------------+-----+-------------+---------------------+----------------------+------------
x3x3o3o    .      ♦  20 |  10  30   0 |  10   0  20   0   0 |   5  0   0   5  0  0 | 32  *  *  *
x3x3o . *b4x4/3*c ♦ 192 |  96 192 192 |  64  96  64  48  48 |  16  8  24   0  8  0 |  * 10  *  *
x . o3o    x4/3*c ♦  16 |   8   0  24 |   0  12   0   0  12 |   0  0   6   0  0  2 |  *  * 40  *
. x3o3o *b4x4/3*c ♦  64 |   0  96  96 |   0   0  64  24  48 |   0   0  0  16  8  8 |  *  *  * 10