Small ditrigonal icosidodecahedron

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Small ditrigonal icosidodecahedron
Small ditrigonal icosidodecahedron.png
Type Uniform star polyhedron
Elements F = 32, E = 60
V = 20 (χ = −8)
Faces by sides 20{3}+12{5/2}
Wythoff symbol 3 | 5/2 3
Symmetry group Ih, [5,3], *532
Index references U30, C39, W70
Dual polyhedron Small triambic icosahedron
Vertex figure Small ditrigonal icosidodecahedron vertfig.png
Bowers acronym Sidtid

In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30. It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram CDel node h3.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png.

It is constructed from Schwarz triangle (3 3 5/2) with Wythoff symbol 3 | 5/2 3, and Coxeter diagram Small ditrigonal icosidodecahedron cd.png. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.

Related polyhedra[edit]

Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the great ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagrammic faces in common), and the regular compound of five cubes.

Small ditrigonal icosidodecahedron.png
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron.png
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron.png
Ditrigonal dodecadodecahedron
Dodecahedron (convex hull)
Compound of five cubes.png
Compound of five cubes
Spherical compound of five cubes.png
Spherical compound of 5 cubes

See also[edit]

External links[edit]