Self-Intersecting Truncated Quasi-Regular Duals
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Medial Disdyakis Triacontahedron
Vertices:
54 (30[4] + 12[10] + 12[10])
Faces:
120 (obtuse triangles)
Edges:
180 (60 short + 60 medium + 60 long)
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle 1 (120):
acos(−9/11)
≈144.903198772 degrees
Dihedral Angle 2 (60):
acos(9/11)
≈215.096801228 degrees
Dual Solid:
Truncated Dodecadodecahedron
(values below based on unit-edge-length Truncated Dodecadodecahedron)
Short Edge (60):
5*(3*sqrt(2)−sqrt(10))/6
≈0.90030252245908817867
Medium Edge (60):
5*(3*sqrt(2)+sqrt(10))/6
≈6.1707652894063870653
Long Edge (60):
2*sqrt(10)
≈6.3245553203367586640
[10]-Vertex Radius (12):
sqrt(5*(5−2*sqrt(5)))
≈1.6245984811645316308
[4]-Vertex Radius (30):
5/3
≈1.6666666666666666667
[10]-Vertex Radius (12):
sqrt(5*(5+2*sqrt(5)))
≈6.8819096023558676910
Edge-scribed Radius:
sqrt(10)/2
≈1.5811388300841896660
Inscribed Radius:
5*sqrt(11)/11
≈1.5075567228888181132