--- Aliases: Complex, Complexes --- #topology #simplex #complex In [[Topology|topological]] terms, a complex refers to a collection of geometric objects called simplices that are glued together in a specific way. A [[Simplex|simplex]] is the most basic building block in a complex and can be thought of as a generalization of a triangle. A complex is formed by taking simplices of different dimensions (points, line segments, triangles, tetrahedra, etc.) and attaching them to each other along their faces. The faces of each simplex are identified with the corresponding faces of other simplices according to certain rules. This gluing process creates a higher-dimensional space that is referred to as the complex. The term "simplex" is often used interchangeably with "complex" in some contexts, but strictly speaking, a simplex refers to an individual geometric object within the complex. In other words, a complex is composed of simplices. In summary, a complex is formed by combining simplices in a specific way through gluing their faces together. The simplex is the basic geometric object within the complex. # References [[@FTDAINTROTOPOLOGICAL2023|Foundations of Topological Data Analysis]]