Acronym ...
Name hyperbolic omnitruncated order 5 dodecahedral tesselation
Circumradius sqrt[-(9+5 sqrt(5))/2] = 3.176503 i
Vertex figure
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Incidence matrix according to Dynkin symbol

x5x3x5x   (N → ∞)

. . . . | 120N |   1   1   1   1 |   1   1   1   1   1   1 | 1  1  1 1
--------+------+-----------------+-------------------------+----------
x . . . |    2 | 60N   *   *   * |   1   1   1   0   0   0 | 1  1  1 0
. x . . |    2 |   * 60N   *   * |   1   0   0   1   1   0 | 1  1  0 1
. . x . |    2 |   *   * 60N   * |   0   1   0   1   0   1 | 1  0  1 1
. . . x |    2 |   *   *   * 60N |   0   0   1   0   1   1 | 0  1  1 1
--------+------+-----------------+-------------------------+----------
x5x . . |   10 |   5   5   0   0 | 12N   *   *   *   *   * | 1  1  0 0
x . x . |    4 |   2   0   2   0 |   * 30N   *   *   *   * | 1  0  1 0
x . . x |    4 |   2   0   0   2 |   *   * 30N   *   *   * | 0  1  1 0
. x3x . |    6 |   0   3   3   0 |   *   *   * 20N   *   * | 1  0  0 1
. x . x |    4 |   0   2   0   2 |   *   *   *   * 30N   * | 0  1  0 1
. . x5x |   10 |   0   0   5   5 |   *   *   *   *   * 12N | 0  0  1 1
--------+------+-----------------+-------------------------+----------
x5x3x .   120 |  60  60  60   0 |  12  30   0  20   0   0 | N  *  * *
x5x . x    20 |  10  10   0  10 |   2   0   5   0   5   0 | * 6N  * *
x . x5x    20 |  10   0  10  10 |   0   5   5   0   0   2 | *  * 6N *
. x3x5x   120 |   0  60  60  60 |   0   0   0  20  30  12 | *  *  * N
or
. . . .    | 60N |   2   2 |   2   2   1   1 | 2  2
-----------+-----+---------+-----------------+-----
x . . .  & |   2 | 60N   * |   1   1   1   0 | 1  2
. x . .  & |   2 |   * 60N |   1   1   0   1 | 2  1
-----------+-----+---------+-----------------+-----
x5x . .  & |  10 |   5   5 | 12N   *   *   * | 1  1
x . x .  & |   4 |   2   2 |   * 30N   *   * | 1  1
x . . x    |   4 |   4   0 |   *   * 15N   * | 0  2
. x3x .    |   6 |   0   6 |   *   *   * 10N | 2  0
-----------+-----+---------+-----------------+-----
x5x3x .  &  120 |  60 120 |  12  30   0  20 | N  *
x5x . x  &   20 |  20  10 |   2   5   5   0 | * 6N

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