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Rhombic Icosahedron

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RhombicIcosahedron

The rhombic icosahedron is a zonohedron which can be derived from the rhombic triacontahedron by removing any one of the zones and bringing together the two pieces into which the remainder of the surface is thereby divided. Its faces are golden rhombi (Kabai 2002, p. 179) and it is one of the five golden isozonohedra.

The rhombic icosahedron is implemented in the Wolfram Language as PolyhedronData["RhombicIcosahedron"].

RhombicIcosahedronNet

A net for the rhombic icosahedron is illustrated above.

The rhombic icosahedron with edge length a has surface area and volume given by

S=8sqrt(5)a^2
(1)
V=2sqrt(5+2sqrt(5))a^3
(2)

and inertia tensor

I=[1/(100)(45+2sqrt(5))Ma^2 0 0; 0 1/(100)(45+2sqrt(5))Ma^2 0; 0 0 1/(25)(10+3sqrt(5))Ma^2].
(3)

See also

Golden Isozonohedron, Golden Rhombus, Rhombic Hexecontahedron, Rhombic Triacontahedron, Zonohedron

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References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 143, 1987.Bilinski, S. "Über die Rhombenisoeder." Glasnik Mat.-Fiz. Astron. Društro Mat. Fiz. Hrvatske Ser. II 15, 251-263, 1960.Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, 2002.Kabai, S. and Bérczi, S. Rhombic Structures: Geometry and Modeling from Crystals to Space Stations. Püsspökladány, Hungary: Uniconstant, 2015.

Referenced on Wolfram|Alpha

Rhombic Icosahedron

Cite this as:

Weisstein, Eric W. "Rhombic Icosahedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RhombicIcosahedron.html

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