Small ditrigonal icosidodecahedron

In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or .

Small ditrigonal icosidodecahedron
TypeUniform star polyhedron
ElementsF = 32, E = 60
V = 20 (χ = 8)
Faces by sides20{3}+12{5/2}
Wythoff symbol3 | 5/2 3
Symmetry groupIh, [5,3], *532
Index referencesU30, C39, W70
Dual polyhedronSmall triambic icosahedron
Vertex figure
(3.5/2)3
Bowers acronymSidtid

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.

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

See also

  • Weisstein, Eric W. "Small ditrigonal icosidodecahedron". MathWorld.
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