Self-Intersecting Truncated Regular Duals
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Great Triakis Icosahedron
Vertices:
32 (20[3] + 12[10])
Faces:
60 (isosceles triangles)
Edges:
90 (60 short + 30 long)
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle:
acos(3*(5*sqrt(5)−8)/61)
≈81.0014100248 degrees
Dual Solid:
Great Stellated Truncated Dodecahedron
(values below based on unit-edge-length Great Stellated Truncated Dodecahedron)
Short Edge (60):
5*(7−sqrt(5))/22
≈1.0827118232955023417
Long Edge (30):
(5−sqrt(5))/2
≈1.3819660112501051518
[3]-Vertex Radius (20):
5*(2*sqrt(15)−3*sqrt(3))/22
≈0.57950324311550042949
[10]-Vertex Radius (12):
sqrt(5*(5−2*sqrt(5)))/2
≈0.81229924058226581539
Edge-scribed Radius:
(3*sqrt(5)−5)/4
≈0.42705098312484227231
Inscribed Radius:
5*sqrt(61*(41−18*sqrt(5)))/122
≈0.27735142326675154997