 This three-dimensional realization of the Desargues configuration is also called the complete pentahedron .The 5-cell or pentatope (a regular simplex in four dimensions) has five vertices, ten edges, ten triangular ridges (2-dimensional faces), and five tetrahedral facets; the edges and ridges touch each other in the same pattern as the Desargues configuration.Extend each of the edges of the 5-cell to the line that contains it (its affine hull), similarly extend each triangle of the 5-cell to the 2-dimensional plane that contains it, and intersect these lines and planes by a three-dimensional hyperplane that neither contains nor is parallel to any of them.