Self-Intersecting Quasi-Regular Duals

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Great Rhombic Triacontahedron
Vertices:  32  (20[3] + 12[5])
Faces:30  (rhombi)
Edges:60  (equal length)
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos((sqrt(5)−1)/4)    72 degrees
Dual Solid:  Great Icosidodecahedron
(values below based on unit-edge-length Great Icosidodecahedron)
Edge Length:  sqrt(10*(5−sqrt(5)))/8    ≈0.65716389014891700753
Rhombus Length:  sqrt(5)/2    ≈1.1180339887498948482
Rhombus Width:  (5−sqrt(5))/4    ≈0.69098300562505257590
[5]-Vertex Radius (12):  sqrt(5*(5−2*sqrt(5)))/4    ≈0.40614962029113290769
[3]-Vertex Radius (20):  (5*sqrt(3)−sqrt(15))/8    ≈0.59840883645462119781
Edge-scribed Radius:  sqrt(5−2*sqrt(5))/2    ≈0.363271264002680442948
Inscribed Radius:  (3*sqrt(5)−5)/8    ≈0.213525491562421136153


References:[1]Edmund Hess, Über vier Archimedeische Polyeder höherer Art,
Schriften der Gesellschaft zur Beförderung der gesammten
Naturwissenschaften zu Marburg 11(4) (1878).
[2]Johann Pitsch, Über Halbreguläre Sternpolyeder, Zeitschrift
für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216.