In geometry, **polyhedra** are associated into pairs called **duals**, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another with equivalent edges. So the regular polyhedra — the Platonic solids and Kepler-Poinsot polyhedra — are arranged into dual pairs, with the exception of the regular tetrahedron which is self-dual.

Duality is also sometimes called *reciprocity* or *polarity*.

In 4-dimensional geometry, a **polyhedral pyramid** is a polychoron constructed by a base polyhedron cell and an apex point. The lateral facets are pyramid cells, each constructed by one face of the base polyhedron and the apex.

The regular 5-cell (or 4-simplex) is an example of a *tetrahedral pyramid*.