Toroidal icosahedron faceting
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|Toroidal icosahedron faceting|
|Bowers style acronym||Toif|
|Faces||6 triangles, 6 pentagons|
|Measures (edge length 1)|
|Convex core||Gyroelongated triangular bipyramid|
|Abstract & topological properties|
|Symmetry||(G2×A1)/2, order 12|
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".