Small ditrigonal icosidodecahedron

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
3D model of a small ditrigonal icosidodecahedron

In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 20 vertices.[1] 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 ​52) with Wythoff symbol 3 | ​52 3. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.

Related polyhedraEdit

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. As a simple polyhedron, it is also a hexakis truncated icosahedron where the triangles touching the pentagons are made coplanar, making the others concave.

a{5,3} a{5/2,3} b{5,5/2}
     =            =            
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron
Dodecahedron (convex hull)
Compound of five cubes
Spherical compound of 5 cubes


  1. ^ Maeder, Roman. "30: small ditrigonal icosidodecahedron". MathConsult.

See alsoEdit

External linksEdit