Acronym ...
Name hyperbolic rhombated order 3 icosahedral tesselation,
hyperbolic cantelated order 3 icosahedral tesselation
 
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Circumradius sqrt[-(43+25 sqrt(5))/22] = 2.120267 i
Vertex figure
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Incidence matrix according to Dynkin symbol

x3o5x3o   (N → ∞)

. . . . | 30N |   2   4 |   1   4   2   2 | 2   2 1
--------+-----+---------+-----------------+--------
x . . . |   2 | 30N   * |   1   2   0   0 | 2   1 0
. . x . |   2 |   * 60N |   0   1   1   1 | 1   1 1
--------+-----+---------+-----------------+--------
x3o . . |   3 |   3   0 | 10N   *   *   * | 2   0 0
x . x . |   4 |   2   2 |   * 30N   *   * | 1   1 0
. o5x . |   5 |   0   5 |   *   * 12N   * | 1   0 1
. . x3o |   3 |   0   3 |   *   *   * 20N | 0   1 1
--------+-----+---------+-----------------+--------
x3o5x .   60 |  60  60 |  20  30  12   0 | N   * *
x . x3o    6 |   3   6 |   0   3   0   2 | * 10N *
. o5x3o   30 |   0  60 |   0   0  12  20 | *   * N

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