Small dodecahemicosahedron - Misplaced Pages

Polyhedron with 22 faces

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	I_h, , *532
Index references	U₆₂, C₇₈, W₁₀₀
Dual polyhedron	Small dodecahemicosacron
Vertex figure	6.5/2.6.5/3
Bowers acronym	Sidhei

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. 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).

Dodecadodecahedron	Small dodecahemicosahedron
Great dodecahemicosahedron	Icosidodecahedron (convex hull)

Traditional filling

Modulo-2 filling

v t e Star-polyhedra navigator
Kepler-Poinsot polyhedra (nonconvex regular polyhedra)	small stellated dodecahedron great dodecahedron great stellated dodecahedron great icosahedron
Uniform truncations of Kepler-Poinsot polyhedra	dodecadodecahedron truncated great dodecahedron rhombidodecadodecahedron truncated dodecadodecahedron snub dodecadodecahedron great icosidodecahedron truncated great icosahedron nonconvex great rhombicosidodecahedron great truncated icosidodecahedron
Nonconvex uniform hemipolyhedra	tetrahemihexahedron cubohemioctahedron octahemioctahedron small dodecahemidodecahedron small icosihemidodecahedron great dodecahemidodecahedron great icosihemidodecahedron great dodecahemicosahedron small dodecahemicosahedron
Duals of nonconvex uniform polyhedra	medial rhombic triacontahedron small stellapentakis dodecahedron medial deltoidal hexecontahedron small rhombidodecacron medial pentagonal hexecontahedron medial disdyakis triacontahedron great rhombic triacontahedron great stellapentakis dodecahedron great deltoidal hexecontahedron great disdyakis triacontahedron great pentagonal hexecontahedron
Duals of nonconvex uniform polyhedra with infinite stellations	tetrahemihexacron hexahemioctacron octahemioctacron small dodecahemidodecacron small icosihemidodecacron great dodecahemidodecacron great icosihemidodecacron great dodecahemicosacron small dodecahemicosacron

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