Self-Intersecting Truncated Regular Duals
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Great Pentakis Dodecahedron
Vertices:
24 (12[5] + 12[10])
Faces:
60 (isosceles triangles)
Edges:
90 (30 short + 60 long)
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle:
acos(−(24−5*sqrt(5))/41)
≈108.220490681 degrees
Dual Solid:
Small Stellated Truncated Dodecahedron
(values below based on unit-edge-length Small Stellated Truncated Dodecahedron)
Short Edge (30):
(3*sqrt(5)−5)/2
≈0.85410196624968454461
Long Edge (60):
5*(1+sqrt(5))/2
≈8.0901699437494742410
[10]-Vertex Radius (12):
sqrt(5*(5−2*sqrt(5)))/2
≈0.81229924058226581539
[5]-Vertex Radius (12):
5*sqrt(5+2*sqrt(5))/2
≈7.6942088429381335064
Edge-scribed Radius:
(5−sqrt(5))/4
≈0.69098300562505257590
Inscribed Radius:
5*sqrt(41*(11−4*sqrt(5)))/82
≈0.55979744948628315994