Editing Hypercube (section)

== {{anchor|Relation to n-simplices}}Relation to (''n''−1)-simplices ==
The graph of the ''n''-hypercube's edges is [[isomorphism|isomorphic]] to the [[Hasse diagram]] of the (''n''−1)-[[simplex]]'s [[Convex polytope#The face lattice|face lattice]]. This can be seen by orienting the ''n''-hypercube so that two opposite vertices lie vertically, corresponding to the (''n''−1)-simplex itself and the null polytope, respectively. Each vertex connected to the top vertex then uniquely maps to one of the (''n''−1)-simplex's facets (''n''−2 faces), and each vertex connected to those vertices maps to one of the simplex's ''n''−3 faces, and so forth, and the vertices connected to the bottom vertex map to the simplex's vertices.

This relation may be used to generate the face lattice of an (''n''−1)-simplex efficiently, since face lattice enumeration algorithms applicable to general polytopes are more computationally expensive.