Acronym ...
Name hyperbolic prismated order 3 icosahedral tesselation,
hyperbolic runcinated order 3 icosahedral tesselation
 
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Circumradius sqrt[-(1+sqrt(5))/2] = 1.272020 i
Vertex figure
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Incidence matrix according to Dynkin symbol

x3o5o3x   (N → ∞)

. . . . | 12N |   5   5 |   5  10   5 | 1   5   5 1
--------+-----+---------+-------------+------------
x . . . |   2 | 30N   * |   2   2   0 | 1   2   1 0
. . . x |   2 |   * 30N |   0   2   2 | 0   1   2 1
--------+-----+---------+-------------+------------
x3o . . |   3 |   3   0 | 20N   *   * | 1   1   0 0
x . . x |   4 |   2   2 |   * 30N   * | 0   1   1 0
. . o3x |   3 |   0   3 |   *   * 20N | 0   0   1 1
--------+-----+---------+-------------+------------
x3o5o .   12 |  30   0 |  20   0   0 | N   *   * *
x3o . x    6 |   6   3 |   2   3   0 | * 10N   * *
x . o3x    6 |   3   6 |   0   3   2 | *   * 10N *
. o5o3x   12 |   0  30 |   0   0  20 | *   *   * N
or
. . . .    | 6N |  10 |  10  10 | 2  10
-----------+----+-----+---------+------
x . . .  & |  2 | 30N |   2   2 | 1   3
-----------+----+-----+---------+------
x3o . .  & |  3 |   3 | 20N   * | 1   1
x . . x    |  4 |   4 |   * 15N | 0   2
-----------+----+-----+---------+------
x3o5o .  &  12 |  30 |  20   0 | N   *
x3o . x  &   6 |   9 |   2   3 | * 10N

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