Compound of ten tetrahedra
|Compound of ten tetrahedra|
(As a compound)
F = 40, E = 60, V = 20
|Symmetry group||icosahedral (Ih)|
|Subgroup restricting to one constituent||chiral tetrahedral (T)|
The compound of ten tetrahedra is one of the five regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron or a compound. This compound was first described by Edmund Hess in 1876.
It can be seen as a faceting of a regular dodecahedron.
As a compound
The compound of five tetrahedra represents two chiral halves of this compound.
As a stellation
|Stellation diagram||Stellation core||Convex hull|
As a facetting
- Regular polytopes, p.98
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
- Coxeter, Harold Scott MacDonald; Du Val, P.; Flather, H. T.; Petrie, J. F. (1999). The fifty-nine icosahedra (3rd ed.). Tarquin. ISBN 978-1-899618-32-3. MR 676126. (1st Edn University of Toronto (1938))
- H.S.M. Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8, 3.6 The five regular compounds, pp.47-50, 6.2 Stellating the Platonic solids, pp.96-104
- Weisstein, Eric W., "Tetrahedron 10-Compound", MathWorld.
- VRML model: 
- Compounds of 5 and 10 Tetrahedra by Sándor Kabai, The Wolfram Demonstrations Project.
- Richard Klitzing, 3D compound, 
|Notable stellations of the icosahedron|
|Regular||Uniform duals||Regular compounds||Regular star||Others|
|(Convex) icosahedron||Small triambic icosahedron||Medial triambic icosahedron||Great triambic icosahedron||Compound of five octahedra||Compound of five tetrahedra||Compound of ten tetrahedra||Great icosahedron||Excavated dodecahedron||Final stellation|
|The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry.|
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