Acronym	sirn
Name	small rhombated penteract, cantellated penteract
Circumradius	sqrt[11+6 sqrt(2)]/2 = 2.207107
Vertex figure	©
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	(is itself convex)
Colonel of regiment	(is itself locally convex – other uniform polyteral members: rawn   & others)
External links

Incidence matrix according to Dynkin symbol

o3o3x3o4x

. . . . . | 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 . x |   4 |   2   2 |   *   * 480  * |   0   0   2  1 |  0  1  2
. . . o4x |   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 . x ♦   6 |   6   3 |   2   0   3  0 |   *   * 320  * |  0  1  1
. . x3o4x ♦  24 |  24  24 |   0   8  12  6 |   *   *   * 40 |  0  0  2
----------+-----+---------+----------------+----------------+---------
o3o3x3o . ♦  10 |  30   0 |  20  10   0  0 |   5   5   0  0 | 32  *  *
o3o3x . x ♦   8 |  12   4 |   8   0   6  0 |   2   0   4  0 |  * 80  *
. o3x3o4x ♦  96 | 192  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10