Editing Polyhedron (section)

=== Orthogonal polyhedron ===
{{main article|Orthogonal polyhedron}}
[[File:Soma_cube_figures.svg|thumb|Some [[orthogonal polyhedra]] made of [[Soma cube]] pieces, themselves [[polycube]]s]]
{{anchor|Orthogonal polyhedra}}Polyhedra are said to be [[orthogonal polyhedra|orthogonal]] because all of their edges are parallel to the axes of a Cartesian coordinate system. This implies that all faces meet at [[right angle]]s, but this condition is weaker: [[Jessen's icosahedron]] has faces meeting at right angles, but does not have axis-parallel edges. Aside from the [[rectangular cuboid]]s, orthogonal polyhedra are nonconvex. They are the three-dimensional analogs of two-dimensional orthogonal polygons, also known as [[rectilinear polygon]]s.  Orthogonal polyhedra are used in [[computational geometry]], where their constrained structure has enabled advances in problems unsolved for arbitrary polyhedra, for example, unfolding the surface of a polyhedron to a [[polygonal net]].<ref>{{citation
 | last = O'Rourke | first = Joseph | author-link = Joseph O'Rourke (professor)
 | contribution = Unfolding orthogonal polyhedra
 | doi = 10.1090/conm/453/08805
 | mr = 2405687
 | pages = 307–317
 | publisher = Amer. Math. Soc., Providence, RI
 | series = Contemp. Math.
 | title = Surveys on discrete and computational geometry
 | volume = 453
 | year = 2008| isbn =978-0-8218-4239-3 | doi-access = free
 }}.</ref> [[Polycube]]s are a special case of orthogonal polyhedra that can be decomposed into identical cubes, and are three-dimensional analogues of planar [[polyomino]]es.<ref>{{citation
 | last = Gardner | first = Martin | author-link = Martin Gardner
 | date = November 1966
 | issue = 5
 | journal = [[Scientific American]]
 | jstor = 24931332
 | pages = 138–143
 | title = Mathematical Games: Is it possible to visualize a four-dimensional figure?
 | volume = 215| doi = 10.1038/scientificamerican1166-138
}}</ref>