Small ditrigonal icosidodecahedron
{{Short description|Polyhedron with 32 faces}}
{{Uniform polyhedra db|Uniform polyhedron stat table|ldID}}
File:Small ditrigonal icosidodecahedron.stl
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.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/30.html|title=30: small ditrigonal icosidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}} It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram {{CDD|node_h3|5|node|3|node}} or {{CDD|label5-2|branch_10ru|split2|node}}.
It is constructed from Schwarz triangle (3 3 {{Frac|5|2}}) with Wythoff symbol 3 | {{Frac|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.
| class="wikitable" width="400" style="vertical-align:top;text-align:center"
!a{5,3} !a{5/2,3} !b{5,5/2} |
| {{CDD|label5-2|branch_10ru|split2|node}} = {{CDD|node_h3|5|node|3|node}}
!{{CDD||label5-4|branch_10ru|split2|node}} = {{CDD|node_h3|5-2|node|3|node}} !File:ditrigonal dodecadodecahedron cd.png = {{CDD|node|5|node_h3|5-2|node}} |
|---|
| align=center
|100px |
| align=center
|100px |100px |
See also
References
{{Reflist}}
External links
- {{mathworld | urlname = SmallDitrigonalIcosidodecahedron| title = Small ditrigonal icosidodecahedron}}