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.