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Great disdyakis dodecahedron

From Wikipedia, the free encyclopedia
Great disdyakis dodecahedron
Type Star polyhedron
Face
Elements F = 48, E = 72
V = 26 (χ = 2)
Symmetry group Oh, [4,3], *432
Index references DU20
dual polyhedron Great truncated cuboctahedron
3D model of a great disdyakis dodecahedron

In geometry, the great disdyakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great truncated cuboctahedron. It has 48 triangular faces.

Proportions

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The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.

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The great disdyakis dodecahedron is topologically identical to the convex Catalan solid, disdyakis dodecahedron, which is dual to the truncated cuboctahedron.

References

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  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
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