Page "Polytope" Paragraph 10

An n-dimensional polytope is bounded by a number of ( n − 1 )- dimensional facets.

These facets are themselves polytopes, whose facets are ( n − 2 )- dimensional ridges of the original polytope.

Every ridge arises as the intersection of two facets ( but the intersection of two facets need not be a ridge ).

Ridges are once again polytopes whose facets give rise to ( n − 3 )- dimensional boundaries of the original polytope, and so on.

These bounding sub-polytopes may be referred to as faces, or specifically j-dimensional faces or j-faces.

A 0-dimensional face is called a vertex, and consists of a single point.

A 1-dimensional face is called an edge, and consists of a line segment.

A 2-dimensional face consists of a polygon, and a 3-dimensional face, sometimes called a cell, consists of a polyhedron.