Compound of ten tetrahedra

Compound of ten tetrahedra
Type	regular compound
Index	UC6, W25
Elements (As a compound)	10 tetrahedra: F = 40, E = 60, V = 20
Dual compound	Self-dual
Symmetry group	icosahedral (Ih)
Subgroup restricting to one constituent	chiral tetrahedral (T)
Stellation diagram Stellation core Convex hull Icosahedron Dodecahedron

This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.

Contents 1 As a compound 2 As a stellation 3 As a facetting 4 See also 5 References 6 External links

As a compound

It can also be seen as the compound of ten tetrahedra with full icosahedral symmetry (I_h). 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.

As a stellation

This polyhedron is a stellation of the icosahedron, and given as Wenninger model index 25.

As a facetting

It is also a facetting of the dodecahedron, as shown at left.

See also

Compound of five tetrahedra

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-52-109859-9. 
• 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. MR676126  (1st Edn University of Toronto (1938))

External links

• Weisstein, Eric W., "Tetrahedron 10-Compound" from MathWorld.
• VRML model: [1]
• Compounds of 5 and 10 Tetrahedra by Sándor Kabai, The Wolfram Demonstrations Project.

Notable stellations of the icosahedron
Regular	Uniform duals		Regular compounds			Regular star	Others
Icosahedron	Small 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.