Compound of ten tetrahedra
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| Compound of ten tetrahedra | |
|---|---|
 |
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| Type | regular compound |
| Stellation core | icosahedron |
| Convex hull | Dodecahedron |
| Index | UC6, W25 |
| Polyhedra | 10 tetrahedra |
| Faces | 40 triangles |
| Edges | 60 |
| Vertices | 20 |
| Dual | Self-dual |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | chiral tetrahedral (T) |
This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.
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[edit] As a compound
It can also be seen as the compound of ten tetrahedra with icosahedral symmetry (Ih). It is one of five regular compounds constructed from identical Platonic solids.
It shares the same vertex arrangement as a dodecahedron.
The compound of five tetrahedra represents two chiral halves of this compound.
[edit] As a stellation
This polyhedron is a stellation of the icosahedron, and given as Wenninger model index 25.
The stellation facets for construction are:
[edit] See also
[edit] References
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-52-109859-9.
[edit] External links
- Eric W. Weisstein, Tetrahedron 10-Compound at MathWorld.
- VRML model: [1]
- Compounds of 5 and 10 Tetrahedra by Sándor Kabai, The Wolfram Demonstrations Project.
