Peak (geometry)

In geometry, a peak is an (n-3)-face of an n-dimensional polytope. A peak attaches at least three facets (and, accordingly, at least three ridges).

A regular n-polytope with Schläfli symbol {p₁,p₂,p₃,...,p_n-2,p_n-1} has a sequence of p_n-1 {p₁,p₂,p₃,...,p_n-2} facets around every peak. For example, the 600-cell, with Schläfli symbol {3,3,5} has 5 {3,3} (tetrahedra) around each peak (edge).

By dimension, this corresponds to:

• a vertex of a polyhedron;
• an edge of a polychoron (4-polytope);
• a face of a 5-polytope;
• a cell of a 6-polytope;
• a 4-face of a 7-polytope;
• and so forth.

External links

• Olshevsky, George, Peak at Glossary for Hyperspace.