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
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

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

Related polyhedra

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)

Gallery

Traditional filling

Modulo-2 filling

See also

• List of uniform polyhedra