Peak (geometry)

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In geometry, a peak is an (n-3)-dimensional element of an n-dimensional polytope.

By dimension, this corresponds to:

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

At least three facets (and, accordingly, at least three ridges) must meet at any peak in a convex polytope.

A regular polytope with Schläfli symbol {p₁,p₂,p₃,...,p_n-2,p_n-1} have a sequence of p_n-1 {p₁,p₂,p₃,...,p_n-2} facets around every peak.

[edit] External links

• Olshevsky, George, Peak at Glossary for Hyperspace.