Self-Intersecting Quasi-Regular Polyhedra

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

(Uniform #54) Great Icosidodecahedron
Vertices:  30  (30[4])
Faces:32  (20 equilateral triangles + 12 regular pentagrams)
Edges:60
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(-sqrt(15*(5-2*sqrt(5)))/15)    ≈100.812316964 degrees
Dual Solid:  Great Rhombic Triacontahedron
(values below based on edge length = 1)
Circumscribed Radius:  (sqrt(5)-1)/2    ≈0.61803398874989484820
Midscribed Radius:  sqrt(5-2*sqrt(5))/2    ≈0.363271264002680442948
Triangle Center Radius:  (3*sqrt(3)-sqrt(15))/6    ≈0.22052817941653583257
Pentagram Center Radius:  sqrt(5*(5-2*sqrt(5)))/5    ≈0.32491969623290632616