Acronym	span
Name	small prismated penteract, runcinated penteract
Circumradius	sqrt(2)+1/2 = 1.914214
Vertex figure	©
Coordinates	((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 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: sirpin   & others)
External links

Incidence matrix according to Dynkin symbol

o3x3o3o4x

. . . . . | 320 |   6   3 |   3   6  12   3 |   3   6   2   6   6  1 |  1  3  3  2
----------+-----+---------+-----------------+------------------------+------------
. x . . . |   2 | 960   * |   1   2   2   0 |   2   2   1   2   1  0 |  1  2  1  1
. . . . x |   2 |   * 480 |   0   0   4   2 |   0   2   0   2   4  1 |  0  1  2  2
----------+-----+---------+-----------------+------------------------+------------
o3x . . . |   3 |   3   0 | 320   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3o . . |   3 |   3   0 |   * 640   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x . . x |   4 |   2   2 |   *   * 960   * |   0   1   0   1   1  0 |  0  1  1  1
. . . o4x |   4 |   0   4 |   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
----------+-----+---------+-----------------+------------------------+------------
o3x3o . . ♦   6 |  12   0 |   4   4   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x . . x ♦   6 |   6   3 |   2   0   3   0 |   * 320   *   *   *  * |  0  1  1  0
. x3o3o . ♦   4 |   6   0 |   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3o . x ♦   6 |   6   3 |   0   2   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x . o4x ♦   8 |   4   8 |   0   0   4   2 |   *   *   *   * 240  * |  0  0  1  1
. . o3o4x ♦   8 |   0  12 |   0   0   0   6 |   *   *   *   *   * 40 |  0  0  0  2
----------+-----+---------+-----------------+------------------------+------------
o3x3o3o . ♦  10 |  30   0 |  10  20   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3o . x ♦  12 |  24   6 |   8   8  12   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x . o4x ♦  12 |  12  12 |   4   0  12   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3o3o4x ♦  64 |  96  96 |   0  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10