Editing Prototile (section)

==Definition==
A tessellation of the plane or of any other space is a cover of the space by [[closed set|closed]] shapes, called tiles, that have [[disjoint sets|disjoint]] [[interior (topology)|interiors]]. Some of the tiles may be [[congruence (geometry)|congruent]] to one or more others. If {{mvar|S}} is the set of tiles in a tessellation, a set {{mvar|R}} of shapes is called a set of prototiles if no two shapes in {{mvar|R}} are congruent to each other, and every tile in {{mvar|S}} is congruent to one of the shapes in {{mvar|R}}.<ref>{{citation|page=7|title=Introductory Tiling Theory for Computer Graphics|series=Synthesis Lectures on Computer Graphics and Animation|first=Craig S.|last=Kaplan|publisher=Morgan & Claypool Publishers|year=2009|isbn=978-1-60845-017-6|url=https://books.google.com/books?id=OPtQtnNXRMMC&pg=PA7}}.</ref>

It is possible to choose many different sets of prototiles for a tiling: translating or rotating any one of the prototiles produces another valid set of prototiles. However, every set of prototiles has the same [[cardinality]], so the number of prototiles is well defined. A tessellation is said to be ''monohedral'' if it has exactly one prototile.