Toroidal icosahedron faceting
Jump to navigation
Jump to search
| Toroidal icosahedron faceting | |
|---|---|
 | |
| Rank | 3 |
| Type | Toroid, orbiform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Toif |
| Elements | |
| Faces | 6 triangles, 6 pentagons |
| Edges | 6+6+12 |
| Vertices | 6+6 |
| Measures (edge length 1) | |
| Circumradius | |
| Central density | 0 |
| Related polytopes | |
| Convex hull | Icosahedron |
| Convex core | Gyroelongated triangular bipyramid |
| Abstract & topological properties | |
| Flag count | 96 |
| Euler characteristic | 0 |
| Orientable | Yes |
| Genus | 1 |
| Properties | |
| Symmetry | (G2×A1)/2, order 12 |
| Convex | No |
The toroidal icosahedron faceting or toif, also called the crazy tube, is an orbiform toroid. As its name suggests, it is a faceting of the icosahedron.
It has the fewest faces and vertices of any known regular faced toroid, with 12 of each. However is not a Stewart toroid as it self-intersects. The record for the fewest faces of a Stewart toroid is 21, with the tunnelled elongated triangular cupola and the record for the fewest vertices is 15, with the tortuous tunnel.
Vertex coordinates[edit | edit source]
Its vertex coordinates are the same as those of the icosahedron.
Gallery[edit | edit source]
External links[edit | edit source]
- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#10 under ike).
- McNeil, Jim. "Simple Stewart toroids".
- Klitzing, Richard. "ike-facetings".