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.

Small dodecahemicosahedron
TypeUniform star polyhedron
ElementsF = 22, E = 60
V = 30 (χ = 8)
Faces by sides12{5/2}+10{6}
Wythoff symbol3 (double covering)
Symmetry groupIh, [5,3], *532
Index referencesU62, C78, W100
Dual polyhedronSmall dodecahemicosacron
Vertex figure
6.5/2.6.5/3
Bowers acronymSidhei
3D model of a small dodecahemicosahedron

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

Small dodecahemicosahedron

Great dodecahemicosahedron

Icosidodecahedron (convex hull)



Traditional filling

Modulo-2 filling

References

  1. Maeder, Roman. "62: small dodecahemicosahedron". MathConsult.

See also


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