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.