Editing Antiprism (section)

===In higher dimensions===
Four-dimensional antiprisms can be defined as having two [[dual polyhedra]] as parallel opposite faces, so that each [[Cell (geometry)|three-dimensional face]] between them comes from two dual parts of the polyhedra: a vertex and a dual polygon, or two dual edges. Every three-dimensional convex polyhedron is combinatorially equivalent to one of the two opposite faces of a four-dimensional antiprism, constructed from its [[canonical polyhedron]] and its polar dual.<ref>{{cite journal | last = Grünbaum | first = Branko | author-link = Branko Grünbaum | issue = 2 | journal = Geombinatorics | mr = 2298896 | pages = 69–78 | title = Are prisms and antiprisms really boring? (Part 3) | url = https://faculty.washington.edu/moishe/branko/BG256.Prisms%20and%20antiprisms.%20Part%203.pdf | volume = 15 | year = 2005}}</ref> However, there exist four-dimensional polychora that cannot be combined with their duals to form five-dimensional antiprisms.<ref>{{cite journal | last = Dobbins | first = Michael Gene | doi = 10.1007/s00454-017-9874-y | issue = 4 | journal = [[Discrete & Computational Geometry]] | mr = 3639611 | pages = 966–984 | title = Antiprismlessness, or: reducing combinatorial equivalence to projective equivalence in realizability problems for polytopes | volume = 57 | year = 2017}}</ref>