Truncated Catalan Solids

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Truncated Pentakis Dodecahedron
(canonical)
version 1
Vertices:  180  (60[3] + 60[3] + 60[3])
Faces:92  (12 regular pentagons + 20 regular hexagons
    + 60 mirror-symmetric hexagons)
Edges:270  (60 short + 60 medium + 150 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on short edge length = 1)
Short Edge (60):  1
Medium Edge (60):  (sqrt(15)−sqrt(3))/2    ≈1.0704662693192697958
Long Edge (150):  sqrt(15)−sqrt(3)−1    ≈1.1409325386385395917
Max Vertex Radius:  sqrt(2*(261+4*sqrt(3)−33*sqrt(5)−4*sqrt(15)))/4    ≈4.7255426485742457752
Edge-scribed Radius:  (21−sqrt(5))/4    ≈4.6909830056250525759
Volume:(405+5100*sqrt(3)+397*sqrt(5)−2180*sqrt(15))/4    ≈420.76860273413047419