Acronym ...
Name hyperbolic omnitruncated order 5 cubical tesselation,
hyperbolic omnitruncated order 4 dodecahedral tesselation
Circumradius sqrt[-18-5 sqrt(2)-14 sqrt(5)-5 sqrt(10)]/2 = 4.248159 i
Vertex figure
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Incidence matrix according to Dynkin symbol

x4x3x5x   (N → ∞)

. . . . | 240N |    1    1    1    1 |   1   1   1   1   1   1 |  1   1   1  1
--------+------+---------------------+-------------------------+--------------
x . . . |    2 | 120N    *    *    * |   1   1   1   0   0   0 |  1   1   1  0
. x . . |    2 |    * 120N    *    * |   1   0   0   1   1   0 |  1   1   0  1
. . x . |    2 |    *    * 120N    * |   0   1   0   1   0   1 |  1   0   1  1
. . . x |    2 |    *    *    * 120N |   0   0   1   0   1   1 |  0   1   1  1
--------+------+---------------------+-------------------------+--------------
x4x . . |    8 |    4    4    0    0 | 30N   *   *   *   *   * |  1   1   0  0
x . x . |    4 |    2    0    2    0 |   * 60N   *   *   *   * |  1   0   1  0
x . . x |    4 |    2    0    0    2 |   *   * 60N   *   *   * |  0   1   1  0
. x3x . |    6 |    0    3    3    0 |   *   *   * 40N   *   * |  1   0   0  1
. x . x |    4 |    0    2    0    2 |   *   *   *   * 60N   * |  0   1   0  1
. . x5x |   10 |    0    0    5    5 |   *   *   *   *   * 24N |  0   0   1  1
--------+------+---------------------+-------------------------+--------------
x4x3x .    48 |   24   24   24    0 |   6  12   0   8   0   0 | 5N   *   *  *
x4x . x    16 |    8    8    0    8 |   2   0   4   0   4   0 |  * 15N   *  *
x . x5x    20 |   10    0   10   10 |   0   5   5   0   0   2 |  *   * 12N  *
. x3x5x   120 |    0   60   60   60 |   0   0   0  20  30  12 |  *   *   * 2N

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