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Rhombic Icosahedron

Vertices:   22  (10[3] + 10[4] + 2[5]) Faces: 20  (rhombi) Edges: 40  (equal length) Symmetry:   5-fold Antiprismatic  (D5v) Dihedral Angle 1 (10):   acos(−(sqrt(5)−1)/4)     108 degrees Dihedral Angle 2 (30):   acos(−(1+sqrt(5))/4)     144 degrees (values below based on edge length = 1) Rhombus Length:   sqrt(10*(5+sqrt(5)))/5     ≈1.7013016167040798644 Rhombus Width:   sqrt(10*(5−sqrt(5)))/5     ≈1.0514622242382672121 [3]-Vertex Radius (10):   sqrt(5)/2     ≈1.1180339887498948482 [4]-Vertex Radius (10):   sqrt(5*(25+8*sqrt(5)))/10     ≈1.4643862847622945006 [5]-Vertex Radius (2):   sqrt(5)/2     ≈1.1180339887498948482 Volume: 2*sqrt(5+2*sqrt(5))     ≈6.1553670743505068051 References: [1] Evgraf Stepanovich Fedorov, An Introduction to the Theory of Figures, Notices of the Imperial Mineralogical Society (St. Petersburg), series 2, 21 (1885), 1-279. [2] Evgraf Stepanovich Fedorov, An Introduction to the Theory of Figures. English translation in Symmetry of Crystals, American Crystallographic Association Monograph 7 (1971), 50-131. [3] Rhombic Icosahedron (Wolfram MathWorld)