Editing Net (polyhedron) (section)

==Higher-dimensional polytope nets==
[[File:tesseract2.svg|thumb|upright|The [[Polycube#Octacube and hypercube unfoldings|Dalí cross]], one of the 261 nets of the [[tesseract]]]]
A net of a [[4-polytope]], a four-dimensional [[polytope]], is composed of polyhedral [[cell (geometry) |cells]] that are connected by their faces and all occupy the same three-dimensional space, just as the polygon faces of a net of a polyhedron are connected by their edges and all occupy the same plane. The net of the tesseract, the four-dimensional [[hypercube]], is used prominently in a painting by [[Salvador Dalí]], ''[[Crucifixion (Corpus Hypercubus)]]'' (1954).<ref>{{citation |last=Kemp |first=Martin |author-link=Martin Kemp (art historian) |title=Dali's dimensions |journal=[[Nature (journal) |Nature]] |volume=391 |issue= 6662 |page=27 |date=1 January 1998 |bibcode=1998Natur.391...27K |s2cid=5317132 |doi=10.1038/34063 |doi-access=free}}</ref> The same tesseract net is central to the plot of the short story [["—And He Built a Crooked House—"]] by [[Robert A. Heinlein]].<ref>{{citation |last=Henderson |first=Linda Dalrymple |author-link=Linda Dalrymple Henderson |editor-last=Emmer |editor-first=Michele |contribution=Science Fiction, Art, and the Fourth Dimension |date=November 2014 |doi=10.1007/978-3-319-01231-5_7 |pages=69–84 |publisher=Springer International Publishing |title=Imagine Math 3: Between Culture and Mathematics|isbn=978-3-319-01230-8 }}</ref>

The number of combinatorially distinct nets of <math>n</math>-dimensional [[hypercube]]s can be found by representing these nets as a tree on <math>2n</math> nodes describing the pattern by which pairs of faces of the hypercube are glued together to form a net, together with a [[perfect matching]] on the [[complement graph]] of the tree describing the pairs of faces that are opposite each other on the folded hypercube. Using this representation, the number of different unfoldings for hypercubes of dimensions 2, 3, 4, ... have been counted as
:1, 11, 261, 9694, 502110, 33064966, 2642657228, ... {{OEIS|id=A091159}}