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.