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.
