Editing Hexahedron (section)

{{Short description|Polyhedron with 6 faces}}
A '''hexahedron''' ({{plural form}}: '''hexahedra''' or '''hexahedrons''') or '''sexahedron''' ({{plural form}}: '''sexahedra''' or '''sexahedrons''') is any [[polyhedron]] with six [[Face (geometry)|faces]]. A [[cube]], for example, is a [[Regular polyhedron|regular]] hexahedron with all its faces [[Square (geometry)|square]], and three squares around each [[Vertex (geometry)|vertex]].

There are seven [[Topology|topologically]] distinct ''convex'' hexahedra,<ref name=dillencourt>{{citation
 | last = Dillencourt | first = Michael B.
 | doi = 10.1006/jctb.1996.0008
 | issue = 1
 | journal = [[Journal of Combinatorial Theory, Series B]]
 | mr = 1368518
 | pages = 87–122
 | title = Polyhedra of small order and their Hamiltonian properties
 | url = https://escholarship.org/uc/item/39f9s8b5
 | volume = 66
 | year = 1996}}</ref> one of which exists in two mirror image forms. Additional non-convex hexahedra exist, with their number depending on how polyhedra are defined. Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.