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