Small ditrigonal icosidodecahedron
| Small ditrigonal icosidodecahedron | |
|---|---|
| File: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} |
| Coxeter diagram | Template:CDD |
| Wythoff symbol | 5/2 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U30, C39, W70 |
| Dual polyhedron | Small triambic icosahedron |
| Vertex figure | File:Small ditrigonal icosidodecahedron vertfig.png (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 Template:CDD or Template:CDD.
It is constructed from Schwarz triangle (3 3 <templatestyles src="Fraction/styles.css" />5⁄2) with Wythoff symbol 3 | <templatestyles src="Fraction/styles.css" />5⁄2 3. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.
Related polyhedra
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} |
|---|---|---|
| Template:CDD = Template:CDD | Template:CDD = Template:CDD | File:Ditrigonal dodecadodecahedron cd.png = Template:CDD |
| File:Small ditrigonal icosidodecahedron.png Small ditrigonal icosidodecahedron |
File:Great ditrigonal icosidodecahedron.png Great ditrigonal icosidodecahedron |
File:Ditrigonal dodecadodecahedron.png Ditrigonal dodecadodecahedron |
| File:Dodecahedron.png Dodecahedron (convex hull) |
File:Compound of five cubes.png Compound of five cubes |
File:Spherical compound of five cubes.png Spherical compound of 5 cubes |
See also
References
External links
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