Acronym	cogrin (old: gocrin)
Name	celligreatorhombated penteract (great cellirhombated penteract), stericantitruncated penteract
Circumradius	sqrt[41+16 sqrt(2)]/2 = 3.988340
Vertex figure	©
Coordinates	((1+3 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
External links

Incidence matrix according to Dynkin symbol

x3o3x3x4x

. . . . . | 1920 |    2    2   1   1 |   1   2   2   2   1   2   2   1 |   1   1   1   2   2   2   1   1  2 |  1  1  1  2  1
----------+------+-------------------+---------------------------------+------------------------------------+---------------
x . . . . |    2 | 1920    *   *   * |   1   1   1   1   0   0   0   0 |   1   1   1   1   1   1   0   0  0 |  1  1  1  1  0
. . x . . |    2 |    * 1920   *   * |   0   1   0   0   1   1   1   0 |   1   0   0   1   1   0   1   1  1 |  1  1  0  1  1
. . . x . |    2 |    *    * 960   * |   0   0   2   0   0   2   0   1 |   0   1   0   2   0   2   1   0  2 |  1  0  1  2  1
. . . . x |    2 |    *    *   * 960 |   0   0   0   2   0   0   2   1 |   0   0   1   0   2   2   0   1  2 |  0  1  1  2  1
----------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o . . . |    3 |    3    0   0   0 | 640   *   *   *   *   *   *   * |   1   1   1   0   0   0   0   0  0 |  1  1  1  0  0
x . x . . |    4 |    2    2   0   0 |   * 960   *   *   *   *   *   * |   1   0   0   1   1   0   0   0  0 |  1  1  0  1  0
x . . x . |    4 |    2    0   2   0 |   *   * 960   *   *   *   *   * |   0   1   0   1   0   1   0   0  0 |  1  0  1  1  0
x . . . x |    4 |    2    0   0   2 |   *   *   * 960   *   *   *   * |   0   0   1   0   1   1   0   0  0 |  0  1  1  1  0
. o3x . . |    3 |    0    3   0   0 |   *   *   *   * 640   *   *   * |   1   0   0   0   0   0   1   1  0 |  1  1  0  0  1
. . x3x . |    6 |    0    3   3   0 |   *   *   *   *   * 640   *   * |   0   0   0   1   0   0   1   0  1 |  1  0  0  1  1
. . x . x |    4 |    0    2   0   2 |   *   *   *   *   *   * 960   * |   0   0   0   0   1   0   0   1  1 |  0  1  0  1  1
. . . x4x |    8 |    0    0   4   4 |   *   *   *   *   *   *   * 240 |   0   0   0   0   0   2   0   0  2 |  0  0  1  2  1
----------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o3x . . ♦   12 |   12   12   0   0 |   4   6   0   0   4   0   0   0 | 160   *   *   *   *   *   *   *  * |  1  1  0  0  0
x3o . x . ♦    6 |    6    0   3   0 |   2   0   3   0   0   0   0   0 |   * 320   *   *   *   *   *   *  * |  1  0  1  0  0
x3o . . x ♦    6 |    6    0   0   3 |   2   0   0   3   0   0   0   0 |   *   * 320   *   *   *   *   *  * |  0  1  1  0  0
x . x3x . ♦   12 |    6    6   6   0 |   0   3   3   0   0   2   0   0 |   *   *   * 320   *   *   *   *  * |  1  0  0  1  0
x . x . x ♦    8 |    4    4   0   4 |   0   2   0   2   0   0   2   0 |   *   *   *   * 480   *   *   *  * |  0  1  0  1  0
x . . x4x ♦   16 |    8    0   8   8 |   0   0   4   4   0   0   0   2 |   *   *   *   *   * 240   *   *  * |  0  0  1  1  0
. o3x3x . ♦   12 |    0   12   6   0 |   0   0   0   0   4   4   0   0 |   *   *   *   *   *   * 160   *  * |  1  0  0  0  1
. o3x . x ♦    6 |    0    6   0   3 |   0   0   0   0   2   0   3   0 |   *   *   *   *   *   *   * 320  * |  0  1  0  0  1
. . x3x4x ♦   48 |    0   24  24  24 |   0   0   0   0   0   8  12   6 |   *   *   *   *   *   *   *   * 80 |  0  0  0  1  1
----------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o3x3x . ♦   60 |   60   60  30   0 |  20  30  30   0  20  20   0   0 |   5  10   0  10   0   0   5   0  0 | 32  *  *  *  *
x3o3x . x ♦   24 |   24   24   0  12 |   8  12   0  12   8   0  12   0 |   2   0   4   0   6   0   0   4  0 |  * 80  *  *  *
x3o . x4x ♦   24 |   24    0  12  12 |   8   0  12  12   0   0   0   3 |   0   4   4   0   0   3   0   0  0 |  *  * 80  *  *
x . x3x4x ♦   96 |   48   48  48  48 |   0  24  24  24   0  16  24  12 |   0   0   0   8  12   6   0   0  2 |  *  *  * 40  *
. o3x3x4x ♦  192 |    0  192  96  96 |   0   0   0   0  64  64  96  24 |   0   0   0   0   0   0  16  32  8 |  *  *  *  * 10