0Simplex
0-simplex, in the context of simplicial geometry, is the simplest kind of simplex: a single point. It is a 0-dimensional object and can be described as the convex hull of one vertex. In a simplicial complex, a 0-simplex corresponds to a vertex, and it has no edges or higher-dimensional faces; its only face is the empty set, sometimes referred to as the (-1)-simplex. The geometric realization of a 0-simplex is just a single point.
More generally, the standard n-simplex Δ^n is the convex hull in R^{n+1} of the standard basis vectors
In algebraic topology, 0-simplices form the basis of the chain groups C_0; oriented 1-simplices have boundaries
Notation and usage: 0-simplex is sometimes denoted Δ^0. It is synonymous with a single vertex or, in