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
(3.5/2)3
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 or CDel label5-2.pngCDel branch 10ru.pngCDel split2.pngCDel node.png.

It is constructed from Schwarz triangle (3 3 5/2) with Wythoff symbol 3 | 5/2 3. 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.

a{5,3} a{5/2,3} b{5,5/2}
CDel label5-2.pngCDel branch 10ru.pngCDel split2.pngCDel node.png = CDel node h3.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png CDel label5-4.pngCDel branch 10ru.pngCDel split2.pngCDel node.png = CDel node h3.pngCDel 5-2.pngCDel node.pngCDel 3.pngCDel node.png CDel node.pngCDel 5.pngCDel node h3.pngCDel 5-2.pngCDel node.png
Small ditrigonal icosidodecahedron.png
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron.png
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron.png
Ditrigonal dodecadodecahedron
Dodecahedron.png
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]