Self-Intersecting Quasi-Regular Duals

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Medial Rhombic Triacontahedron

Vertices:   24  (12[5] + 12[5]) Faces: 30  (rhombi) Edges: 60  (equal length) Symmetry:   Full Icosahedral  (Ih) Dihedral Angle:   acos(−1/2)     120 degrees Dual Solid:   Dodecadodecahedron (values below based on unit-edge-length Dodecadodecahedron) Edge Length:   3*sqrt(3)/4     ≈1.2990381056766579701 Rhombus Length:   3*(1+sqrt(5))/4     ≈2.4270509831248422723 Rhombus Width:   3*(sqrt(5)−1)/4     ≈0.92705098312484227231 Inner Vertex Radius (12):   3*sqrt(2*(5−sqrt(5)))/8     ≈0.881677878438709693753 Outer Vertex Radius (12):   3*sqrt(2*(5+sqrt(5)))/8     ≈1.4265847744427303582 Edge-scribed Radius:   sqrt(3)/2     ≈0.86602540378443864676 Inscribed Radius:   3/4     0.75 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.