Other Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

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)