Acronym ...
Name hyperbolic birectified alternated order-5 cubic tesselation,
hyperbolic runcic order-5 cubic tesselation
Circumradius sqrt[-(7+5 sqrt(5))/8] = 1.507495 i
Vertex figure
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Incidence matrix according to Dynkin symbol

x3o3o *b5x   (N → ∞)

. . .    . | 20N |   3   3 |   3   3   3 |  1 3 1
-----------+-----+---------+-------------+-------
x . .    . |   2 | 30N   * |   2   1   0 |  1 2 0
. . .    x |   2 |   * 30N |   0   1   2 |  0 2 1
-----------+-----+---------+-------------+-------
x3o .    . |   3 |   3   0 | 20N   *   * |  1 1 0
x . .    x |   4 |   2   2 |   * 15N   * |  0 2 0
. o . *b5x |   5 |   0   5 |   *   * 12N |  0 1 1
-----------+-----+---------+-------------+-------
x3o3o    .    4 |   6   0 |   4   0   0 | 5N * *
x3o . *b5x   60 |  60  60 |  20  30  12 |  * N *
. o3o *b5x   20 |   0  30 |   0   0  12 |  * * N

s4o3o5x   (N → ∞)

demi( . . . . ) | 20N |   3   3 |   3   3   3 | 1  1 3
----------------+-----+---------+-------------+-------
demi( . . . x ) |   2 | 30N   * |   2   1   0 | 1  0 2
      s4o . .   |   2 |   * 30N |   0   1   2 | 0  1 2
----------------+-----+---------+-------------+-------
demi( . . o5x ) |   5 |   5   0 | 12N   *   * | 1  0 1
      s4o 2 x   |   4 |   2   2 |   * 15N   * | 0  0 2
sefa( s4o3o . ) |   3 |   0   3 |   *   * 20N | 0  1 1
----------------+-----+---------+-------------+-------
demi( . o3o5x )   20 |  30   0 |  12   0   0 | N  * *
      s4o3o .      4 |   0   6 |   0   0   4 | * 5N *
sefa( s4o3o5x )   60 |  60  60 |  12  30  20 | *  * N

starting figure: x4o3o5x

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