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Rhombic Enneacontahedron

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RhombicEnneacontahedron

The rhombic enneacontahedron is the equilateral zonohedron constructed from the 10 diameters of the dodecahedron. This enneacontahedron somewhat resembles a figure of Sharp (Ball and Coxeter 1987).

RhombicEnneacontahedronFaces

It has 90 faces, with 30 of one type and the other 60 of another.

It is implemented in the Wolfram Language as PolyhedronData["RhombicEnneacontahedron"].

The rhombic enneacontahedron with edge length a has surface area and volume

S=20(1+2sqrt(2))a^2
(1)
V=(20)/3sqrt(43+(56)/3sqrt(5))a^3
(2)

and, for uniform mass density and total mass M, moment of inertia about its center is the tensor

I=1/(465)(619+222sqrt(5))Ma^2[1 0 0; 0 1 0; 0 0 1].
(3)

The rhombic enneacontahedron has Dehn invariant 0.

See also

Enneacontahedron, Equilateral Zonohedron

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References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 142-143, 1987.Sharp, A. Geometry Improv'd: 1. By a Large and Accurate Table of Segments of Circles, with Compendious Tables for Finding a True Proportional Part, Exemplify'd in Making out Logarithms from them, there Being a Table of them for all Primes to 1100, True to 61 Figures. 2. A Concise Treatise of Polyhedra, or Solid Bodies, of Many Bases. London, England: R. Mount, p. 87, 1717.Towle, R. "Graphics Gallery: Polar Zonohedra." Mathematica J. 6, 8-12, 1996. https://library.wolfram.com/infocenter/Articles/3335/.

Referenced on Wolfram|Alpha

Rhombic Enneacontahedron

Cite this as:

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

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