ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: An n-simplex is ${\displaystyle n}$ -dimensional, and is topological isomorphic to an ${\displaystyle n}$ -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 ${\displaystyle n}$ -simplex boundary will have ${\displaystyle n\left(n-1\right)}$ -simplexes. An ${\displaystyle n}$ -simplex and an ${\displaystyle n}$ -disc are topologically isomorphic. The boundary of an ${\displaystyle n}$ -simplex is isomorphic to an ${\displaystyle \left(n-1\right)}$ -sphere. In all cases, the number prefix represents the topological dimension of the object.