Compound of ten tetrahedra

It can be seen as a faceting of a regular dodecahedron.

As a compound

It can also be seen as the

It shares the same vertex arrangement as a dodecahedron.

The compound of five tetrahedra represents two chiral halves of this compound (it can therefore be seen as a "compound of two compounds of five tetrahedra").

It can be made from the

As a stellation

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

Stellation diagram	Stellation core	Convex hull
	Icosahedron	Dodecahedron

As a facetting

It is also a

If it is treated as a simple non-convex polyhedron without self-intersecting surfaces, it has 180 faces (120 triangles and 60 concave quadrilaterals), 122 vertices (60 with degree 3, 30 with degree 4, 12 with degree 5, and 20 with degree 12), and 300 edges, giving an Euler characteristic of 122-300+180 = +2.

See also

• Compound of five tetrahedra

References

• ISBN 0-521-09859-9
  .
• MR 0676126
  . (1st Edn University of Toronto (1938))
• 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: [1]
• Compounds of 5 and 10 Tetrahedra by Sándor Kabai,
  The Wolfram Demonstrations Project
  .
• Klitzing, Richard. "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 compounds with icosahedral symmetry .

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