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Small dodecahemicosahedron

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Small dodecahemicosahedron
Type Uniform star polyhedron
Elements F = 22, E = 60
V = 30 (χ = −8)
Faces by sides 12{5/2}+10{6}
Coxeter diagram
Wythoff symbol 5/3 5/2 | 3 (double covering)
Symmetry group Ih, [5,3], *532
Index references U62, C78, W100
Dual polyhedron Small dodecahemicosacron
Vertex figure
6.5/2.6.5/3
Bowers acronym Sidhei
3D model of a small dodecahemicosahedron

In geometry, the small dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.

It is a hemipolyhedron with ten hexagonal faces passing through the model center.

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Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the dodecadodecahedron (having the pentagrammic faces in common), and with the great dodecahemicosahedron (having the hexagonal faces in common).


Dodecadodecahedron

Small dodecahemicosahedron

Great dodecahemicosahedron

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. "62: small dodecahemicosahedron". MathConsult.
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