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Small Rhombihexahedron


U18

The small rhombihexahedron is the uniform polyhedron with Maeder index 18 (Maeder 1997), Wenninger index 86 (Wenninger 1989), Coxeter index 60 (Coxeter et al. 1954), and Har'El index 23 (Har'El 1993). It has Wythoff symbol 3/224| and its faces are 12{4}+6{8}. It is a faceted version of the small rhombicuboctahedron.

The small rhombihexahedron is implemented in the Wolfram Language as UniformPolyhedron[86], UniformPolyhedron["SmallRhombihexahedron"], UniformPolyhedron[{"Coxeter", 60}], UniformPolyhedron[{"Kaleido", 23 }], UniformPolyhedron[{"Uniform", 18}], or UniformPolyhedron[{"Wenninger", 86}]. It is also implemented in the Wolfram Language as PolyhedronData["SmallRhombihexahedron"].

SmallRhombicuboctahedralGraph

Its skeleton is the small rhombicuboctahedral graph, illustrated above.

Its circumradius for unit edge lengths is

 R=1/2sqrt(5+2sqrt(2)).

Its dual polyhedron is the small rhombihexacron.

U18Hull

The convex hull of the small rhombihexahedron is the Archimedean small rhombicuboctahedron A_6, whose dual is the deltoidal icositetrahedron, so the dual of the small rhombihexahedron (i.e., the small rhombihexacron) is one of the stellations of the deltoidal icositetrahedron (Wenninger 1971, p. 57).


See also

Uniform Polyhedron

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References

Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy. Soc. London Ser. A 246, 401-450, 1954.Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "18: Small Rhombihexahedron." 1997. https://www.mathconsult.ch/static/unipoly/18.html.Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 134, 1971.

Referenced on Wolfram|Alpha

Small Rhombihexahedron

Cite this as:

Weisstein, Eric W. "Small Rhombihexahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmallRhombihexahedron.html

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