n-simplex <geometry, topology>
convex hull of n+1 points in general position in a space of dimension at least n, or a topologically isomorphic image of such a geometry
Note to entry: An n-simplex is n-dimensional, and is topological isomorphic to an n-disc. A 0-simplex is a point. A 1-simplex is a curve (usually a line) with two 0-simplexes (points) on its boundary; a 2-simplex is a triangular surface with three 1-simplices on its boundary. In general, an n-simplex boundary will have n (n−1)-simplexes. An n-simplex and an n-disc are topologically isomorphic. The boundary of an n-simplex is isomorphic to an (n−1)-sphere. In all cases, the number prefix represents the topological dimension of the object.
ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)