Compound of ten tetrahedra
|Compound of ten tetrahedra|
|Bowers style acronym||E|
|Faces||40 triangles as 20 golden hexagrams|
|Vertex figure||Golden hexagram, edge length 1|
|Measures (edge length 1)|
|Number of external pieces||180|
|Level of complexity||10|
|Army||Doe, edge length|
|Dual||Compound of ten tetrahedra|
|Conjugate||Compound of ten tetrahedra|
|Abstract & topological properties|
|Symmetry||H3, order 120|
The icosicosahedron, e, or compound of ten tetrahedra is a weakly-regular polyhedron compound. It consists of 40 triangles which form 20 coplanar pairs, combining into golden hexagrams. The vertices also coincide in pairs, leading to 20 vertices where 6 triangles join. It can be seen as a compound of the two chiral forms of the chiricosahedron. It can also be seen as a rhombihedron, the compound of five cubes, with each cube replaced by a stella octangula.
This compound is sometimes considered to be regular, but it is not flag-transitive, despite the fact it is vertex, edge, and face-transitive. It is however regular if you consider conjugacies along with its other symmetries.
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an icosicosahedron of edge length 1 are given by:
plus all even permutations of:
Related polyhedra[edit | edit source]
It has connections to all weakly regular polyhedra and polyhedron compounds. It can be decomposed into 10 tetrahedra, 5 stella octangulas, or 2 chiricosahedra. It and each chiricosahedron has a dodecahedron convex hull and an icosahedron convex core while each stella octangula has a cube convex hull and an octahedron convex core, which form a rhombihedron and small icosicosahedron respectively.
[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category C1: Compound Regulars" (#3).
- Klitzing, Richard. "e".
- Wikipedia Contributors. "Compound of ten tetrahedra".