Small dodecahemicosahedron

Small dodecahemicosahedron
File:Small dodecahemicosahedron.png
Type	Uniform star polyhedron
Elements	F = 22, E = 60 V = 30 (χ = −8)
Faces by sides	12{5/2}+10{6}
Coxeter diagram	Template:CDD
Wythoff symbol	3 (double covering)
Symmetry group	I_h, [5,3], *532
Index references	U₆₂, C₇₈, W₁₀₀
Dual polyhedron	Small dodecahemicosacron
Vertex figure	File:Small dodecahemicosahedron vertfig.png 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.

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).

File:Dodecadodecahedron.png Dodecadodecahedron	File:Small dodecahemicosahedron.png Small dodecahemicosahedron
File:Great dodecahemicosahedron.png Great dodecahemicosahedron	File:Icosidodecahedron.png Icosidodecahedron (convex hull)

File:Small dodecahemicosahedron.png Traditional filling	File:Small dodecahemicosahedron 2.png Modulo-2 filling