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Snub Dodecadodecahedron

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U40

The snub dodecadodecahedron, not to be confused with the Archimdean snub dodecahedron, is the uniform polyhedron is the uniform polyhedron with Maeder index 40 (Maeder 1997), Wenninger index 111 (Wenninger 1989), Coxeter index 49 (Coxeter et al. 1954), and Har'El index 45 (Har'El 1993). It has Wythoff symbol |25/25. Its faces are 12{5/2}+60{3}+12{5}.

The snub dodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[111], UniformPolyhedron["SnubDodecadodecahedron"], UniformPolyhedron[{"Coxeter", 49}], UniformPolyhedron[{"Kaleido", 45}], UniformPolyhedron[{"Uniform", 40}], or UniformPolyhedron[{"Wenninger", 111}]. It is also implemented in the Wolfram Language as PolyhedronData["SnubDodecadodecahedron"].

It has circumradius for unit edge length of

R=1.274439882...

(Coxeter et al. 1954).

Its dual polyhedron is the medial pentagonal hexecontahedron.

See also

Snub Dodecadodecahedral Graph, Uniform Polyhedron

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References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 139, 1987.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.Cundy, H. and Rollett, A. "Snub Dodecahedron. 3^4.5." §3.7.13 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 114-115, 1989.Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "40: Snub Dodecadodecahedron." 1997. https://www.mathconsult.ch/static/unipoly/40.html.Wenninger, M. J. "Snub Dodecadodecahedron." Model 111 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 174-176, 1971.

Referenced on Wolfram|Alpha

Snub Dodecadodecahedron

Cite this as:

Weisstein, Eric W. "Snub Dodecadodecahedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SnubDodecadodecahedron.html

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