A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron
5-compounds of opposite chirality combined.

The vertices of the first tetrahedron 10-compound are among the vertices of the dodecahedron-icosahedron compound
and great stellated dodecahedron .

The tetrahedron 10-compounds illustrated above are implemented in the Wolfram Language as PolyhedronData ["TetrahedronTenCompound" ,
n ]
for
and 2.

These tetrahedron 10-compounds are illustrated above together with their duals
and common midspheres .

The common solids and convex hulls are illustrated above. For the first compound, the interior is a regular
icosahedron and the convex hull is a regular
dodecahedron . For the second, the interior is a square-augmented cuboctahedron
and the convex hull is a chamfered
cube .

The tetrahedron 10-compound can be inscribed in the vertices of an augmented dodecahedron , (first) cube 4-compound , cube-octahedron 5-compound , augmented dodecahedron , deltoidal
hexecontahedron , disdyakis triacontahedron ,
dodecahedron , echidnahedron ,
great rhombic triacontahedron , great stellated dodecahedron , metabiaugmented
dodecahedron , parabiaugmented dodecahedron ,
pentagonal hexecontahedron , pentakis
dodecahedron , rhombic enneacontahedron ,
rhombic hexecontahedron , rhombic
triacontahedron , small triambic icosahedron ,
spikey , triakis icosahedron ,
and triaugmented dodecahedron (E. Weisstein,
Dec. 25-28, 2009).

See also Polyhedron Compound ,

Regular
Polyhedron
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References Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 135, 1987. Cundy,
H. and Rollett, A. "Ten Tetrahedra in a Dodecahedron." §3.10.9 in
Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 141-142, 1989. Wenninger,
M. J. Polyhedron
Models. New York: Cambridge University Press, p. 45, 1989.
Cite this as:
Weisstein, Eric W. "Tetrahedron 10-Compound."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Tetrahedron10-Compound.html

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