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Great dodecahemidodecahedron

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Great dodecahemidodecahedron
Type Uniform star polyhedron
Elements F = 18, E = 60
V = 30 (χ = −12)
Faces by sides 12{5/2}+6{10/3}
Coxeter diagram
Wythoff symbol 5/3 5/2 | 5/3 (double covering)
Symmetry group Ih, [5,3], *532
Index references U70, C86, W107
Dual polyhedron Great dodecahemidodecacron
Vertex figure
5/2.10/3.5/3.10/3
Bowers acronym Gidhid
3D model of a great dodecahemidodecahedron

In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.

Aside from the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}, it is the only nonconvex uniform polyhedron whose faces are all non-convex regular polygons (star polygons), namely the star polygons {5/2} and {10/3}.

It is a hemipolyhedron with 6 decagrammic faces passing through the model center.

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Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the pentagrammic faces in common) and the great icosihemidodecahedron (having the decagrammic faces in common).


Great icosidodecahedron

Great dodecahemidodecahedron

Great icosihemidodecahedron

Icosidodecahedron (convex hull)
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Traditional filling

Modulo-2 filling

See also

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References

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  1. ^ Maeder, Roman. "70: great dodecahemidodecahedron". MathConsult.
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