In mathematics, a polyhedral complex is a set of polyhedra in a real vector space that fit together in a specific way.
[1] Polyhedral complexes generalize simplicial complexes and arise in various areas of polyhedral geometry, such as tropical geometry, splines and hyperplane arrangements.
is a set of polyhedra that satisfies the following conditions: Note that the empty set is a face of every polyhedron, and so the intersection of two polyhedra in
A fan is a polyhedral complex in which every polyhedron is a cone from the origin.
Examples of fans include: