Acronym ...
Name hyperbolic rectified order 5 cubic tesselation
Circumradius sqrt[-sqrt(5)/2] = 1.057371 i
Vertex figure
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Incidence matrix according to Dynkin symbol

o4x3o5o   (N → ∞)

. . . . | 12N   10 |   5  10 |  5  2
--------+-----+-----+---------+------
. x . . |   2 | 60N |   1   2 |  2  1
--------+-----+-----+---------+------
o4x . . |   4 |   4 | 15N   * |  2  0
. x3o . |   3 |   3 |   * 40N |  1  1
--------+-----+-----+---------+------
o4x3o .   12 |  24 |   6   8 | 5N  *
. x3o5o   12 |  30 |   0  20 |  * 2N

x3o3x *b5o   (N → ∞)

. . .    . | 12N    5   5 |   5   5   5 |  5 1 1
-----------+-----+---------+-------------+-------
x . .    . |   2 | 30N   * |   1   2   0 |  2 1 0
. . x    . |   2 |   * 30N |   1   0   2 |  2 0 1
-----------+-----+---------+-------------+-------
x . x    . |   4 |   2   2 | 15N   *   * |  2 0 0
x3o .    . |   3 |   3   0 |   * 20N   * |  1 1 0
. o3x    . |   3 |   0   3 |   *   * 20N |  1 0 1
-----------+-----+---------+-------------+-------
x3o3x    .   12 |  12  12 |   6   4   4 | 5N * *
x3o . *b5o   12 |  30   0 |   0  20   0 |  * N *
. o3x *b5o   12 |   0  30 |   0   0  20 |  * * N

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