In the context of the theory and computation of fixed points of continuous mappings, researchers have developed combinatorial analogs of Brouwer's fixed-point theorem on the simplex and on the n-cube.

The n-skeleton of a (2n + 2)-simplex does not embed in R2n. This well-known result is due (independently) to van Kampen, 1932, and Flores, 1933, who proved the case p = 2 of the following: Theorem.