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