Compound of five tetrahedra

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

As a compound

It can be constructed by arranging five

It shares the same vertex arrangement as a regular dodecahedron.

There are two enantiomorphous forms (the same figure but having opposite chirality) of this compound polyhedron. Both forms together create the reflection symmetric compound of ten tetrahedra.

It has a

spherical tiling

Transparent Models (Animation)

Five interlocked tetrahedra

As a stellation

It can also be obtained by stellating the icosahedron, and is given as Wenninger model index 24.

Stellation diagram	Stellation core	Convex hull
	Icosahedron	Dodecahedron

As a faceting

It is a faceting of a dodecahedron, as shown at left.

Group theory

The compound of five tetrahedra is a geometric illustration of the notion of

The symmetry group of the compound is the (rotational)

An unusual dual property

This compound is unusual, in that the

• Compound of ten tetrahedra
• Compound of five cubes
• Compound of five truncated tetrahedra

References

• ISBN 0-521-09859-9
  .
• ISBN 0-486-61480-8
  , 3.6 The five regular compounds, pp.47-50, 6.2 Stellating the Platonic solids, pp.96-104
• MR 0676126
  . (1st Edn University of Toronto (1938))

• Weisstein, Eric W. "Tetrahedron 5-Compound". MathWorld.
• Metal Sculpture of Five Tetrahedra Compound
• 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 .