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Great icosihemidodecahedron

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Great icosihemidodecahedron
Type Uniform star polyhedron
Elements F = 26, E = 60
V = 30 (χ = −4)
Faces by sides 20{3}+6{10/3}
Coxeter diagram
Wythoff symbol 3/2 3 | 5/3
Symmetry group Ih, [5,3], *532
Index references U71, C85, W106
Dual polyhedron Great icosihemidodecacron
Vertex figure
3.10/3.3/2.10/3
Bowers acronym Geihid
3D model of a great icosihemidodecahedron

In geometry, the great icosihemidodecahedron (or great icosahemidodecahedron) is a nonconvex uniform polyhedron, indexed as U71. It has 26 faces (20 triangles and 6 decagrams), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.

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 triangular faces in common), and with the great dodecahemidodecahedron (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. "71: great icosihemidodecahedron". MathConsult.
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