Editing Simplex (section)

=== Relation to the (''n'' + 1)-hypercube ===
The [[Hasse diagram]] of the face lattice of an {{mvar|n}}-simplex is isomorphic to the graph of the {{math|(''n'' + 1)}}-[[hypercube]]'s edges, with the hypercube's vertices mapping to each of the {{mvar|n}}-simplex's elements, including the entire simplex and the null polytope as the extreme points of the lattice (mapped to two opposite vertices on the hypercube). This fact may be used to efficiently enumerate the simplex's face lattice, since more general face lattice enumeration algorithms are more computationally expensive.

The {{mvar|n}}-simplex is also the [[vertex figure]] of the {{math|(''n'' + 1)}}-hypercube. It is also the [[Facet (geometry)|facet]] of the {{math|(''n'' + 1)}}-[[orthoplex]].