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Great Rhombihexahedron


U21

The great rhombihexahedron is the uniform polyhedron with Maeder index 21 (Maeder 1997), Wenninger index 103 (Wenninger 1989), Coxeter index 82 (Coxeter et al. 1954), and Har'El index 26 (Har'El 1993). Its Wythoff symbol is 24/33/2; 4/2| and its faces are 12{4}+6{8/3}.

The great rhombihexahedron is implemented in the Wolfram Language as UniformPolyhedron[103], UniformPolyhedron["GreatRhombihexahedron"], UniformPolyhedron[{"Coxeter", 82}], UniformPolyhedron[{"Kaleido", 26}], UniformPolyhedron[{"Uniform", 21}], or UniformPolyhedron[{"Wenninger", 103}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatRhombihexahedron"].

SmallRhombicuboctahedralGraph

The skeleton of the tgreat rhombihexahedron is the small rhombicuboctahedral graph, illustrated above.

The circumradius for a great rhombihexahedron of unit edge length is

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

Its dual is the great rhombihexacron.

U21Hull

The convex hull of the great rhombihexahedron is the Archimedean truncated cube A_9, whose dual is the small triakis octahedron, so the dual of the great rhombihexahedron (i.e., the great rhombihexacron) is one of the stellations of the small triakis octahedron (Wenninger 1983, 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. "21: Great Rhombihexahedron." 1997. https://www.mathconsult.ch/static/unipoly/21.html.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 57 and 160, 1983.Wenninger, M. J. "Great Rhombihexahedron." Model 103 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 159-160, 1989.

Referenced on Wolfram|Alpha

Great Rhombihexahedron

Cite this as:

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

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