An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a axes aligned along the -axis and rotating them a sixth of a turn with respect to each
other.

This compound is implemented in the Wolfram Language as PolyhedronData ["TetrahedronThreeCompound" ,
1 ].

This tetrahedron 3-compound is illustrated above together with its cube
3-compound dual and common midsphere .

The common solid is a 6-trapezohedron and the convex hull is (non-equilateral) a 6-antiprism .

See also Polyhedron Compound ,

Regular
Tetrahedron
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References Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant,
p. 128, 2002.
Cite this as:
Weisstein, Eric W. "Tetrahedron 3-Compound."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Tetrahedron3-Compound.html

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