Small dodecahemicosahedron

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Small dodecahemicosahedron
Small dodecahemicosahedron.png
Type Uniform star polyhedron
Elements F = 22, E = 60
V = 30 (χ = 8)
Faces by sides12{5/2}+10{6}
Wythoff symbol 5/3 5/2 | 3 (double covering)
Symmetry group Ih, [5,3], *532
Index references U 62, C 78, W 100
Dual polyhedron Small dodecahemicosacron
Vertex figure Small dodecahemicosahedron vertfig.png
6.5/2.6.5/3
Bowers acronym Sidhei
3D model of a small dodecahemicosahedron Small dodecahemicosahedron.stl
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.

Contents

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

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.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Icosidodecahedron.png
Icosidodecahedron (convex hull)
Small dodecahemicosahedron.png
Traditional filling
Small dodecahemicosahedron 2.png
Modulo-2 filling

See also

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In geometry, the small dodecahemicosacron is the dual of the small dodecahemicosahedron, and is one of nine dual hemipolyhedra. It appears visually indistinct from the great dodecahemicosacron.

References

  1. Maeder, Roman. "62: small dodecahemicosahedron". MathConsult.{{cite web}}: CS1 maint: url-status (link)