Fivedimensional

Fivedimensional is an adjective used to describe objects, spaces, or theories that involve five independent coordinates or dimensions. In mathematics, five-dimensional space is typically modeled as real five-dimensional space, denoted R^5, whose points are given by five coordinates (x1, x2, x3, x4, x5). The standard Euclidean metric defines the distance between two points as the square root of the sum of squared coordinate differences. In this context, geometric figures, volumes, and other properties generalize familiar three- and four-dimensional concepts to higher dimensions.

Common five-dimensional objects include the five-dimensional hypercube (the 5-cube) and the five-simplex. The 5-cube consists of all points with coordinates in a fixed range, producing a regular five-dimensional analogue of a cube. The five-simplex is the convex hull of six affinely independent points and serves as the simplest five-dimensional generalization of a triangle and a tetrahedron. Other five-dimensional polytopes also exist, including the five-dimensional cross-polytope, which is the 5D analogue of the octahedron.

In physics, five dimensions have played a historical role in theories that extend spacetime beyond the familiar four dimensions. Kaluza–Klein theory famously explored a fifth dimension to unify gravity with electromagnetism, while various braneworld scenarios consider extra spatial dimensions that may be compactified or otherwise hidden from direct observation. In mathematics and its applications, five-dimensional models also arise in data analysis, topology, and the study of Lie groups such as SO(5).