Editing Fundamental domain (section)

{{Short description|Subset of a space that contains exactly one point from each orbit of the action of a group}}
{{More citations needed|date=August 2018}}

Given a [[topological space]] and a [[group (mathematics)|group]] [[Group action (mathematics)|acting]] on it, the images of a single point under the group action form an [[Group action (mathematics)#Orbits_and_stabilizers|orbit]] of the action. A '''fundamental domain''' or '''fundamental region''' is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.

There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a [[connected space|connected]] subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then [[tessellation|tile]] the space. One general construction of fundamental domains uses [[Voronoi cell]]s.