Compound of four tetrahedra
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In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a compound
Polyhedral compound
A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram....

 of three tetrahedra
can be constructed by three tetrahedra in a number of different symmetry positions.

One compound can be constructed rotating a tetrahedron by 45 degree turns along an axis of the middle of an edge. It has dihedral symmetry, D4
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