Small ditrigonal icosidodecahedron | |
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Type | Uniform star polyhedron |
Elements | F = 32, E = 60 V = 20 (χ = −8) |
Faces by sides | 20{3}+12{5/2} |
Coxeter diagram | ![]() ![]() ![]() ![]() |
Wythoff symbol | 3 | 5/2 3 |
Symmetry group | Ih, [5,3], *532 |
Index references | U30, C39, W70 |
Dual polyhedron | Small triambic icosahedron |
Vertex figure |
![]() (3.5/2)3 |
Bowers acronym | Sidtid |
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 or
.
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} |
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![]() Small ditrigonal icosidodecahedron |
![]() Great ditrigonal icosidodecahedron |
![]() Ditrigonal dodecadodecahedron |
![]() Dodecahedron ( convex hull) |
![]() Compound of five cubes |
![]() Spherical compound of 5 cubes |