Ditrigonal Dodecadodecahedron


The ditrigonal dodecadodecahedron, also called the ditrigonal dodecahedron, is the uniform polyhedron with Maeder index 41 (Maeder 1997), Wenninger index 80 (Wenninger 1989), Coxeter index 53 (Coxeter et al. 1954), and Har'El index 46 (Har'El 1993). It has Wythoff symbol 3|5/35 and its faces are 12{5/2}+12{5}. It is a faceted version of the small ditrigonal icosidodecahedron.

The ditrigonal dodecadodecahedron is implemented in the Wolfram Language as UniformPolyhedron[80], UniformPolyhedron["DitrigonalDodecadodecahedron"], UniformPolyhedron[{"Coxeter", 53}], UniformPolyhedron[{"Kaleido", 46}], UniformPolyhedron[{"Uniform", 41}], or UniformPolyhedron[{"Wenninger", 80}]. It is also implemented in the Wolfram Language as PolyhedronData["DitrigonalDodecadodecahedron"].

The convex hull is a regular dodecahedron and the cube 5-compound and tetrahedron 10-compound can be constructed from its vertices.

Its circumradius for unit edge length is


Its dual polyhedron is the medial triambic icosahedron.

See also

Cube 5-Compound, Uniform Polyhedron

Explore with Wolfram|Alpha


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. "41: Ditrigonal Dodecadodecahedron." 1997., M. J. "Ditrigonal Dodecadodecahedron." Model 80 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 123-124, 1989.

Referenced on Wolfram|Alpha

Ditrigonal Dodecadodecahedron

Cite this as:

Weisstein, Eric W. "Ditrigonal Dodecadodecahedron." From MathWorld--A Wolfram Web Resource.

Subject classifications