Euclidean tilings by convex regular polygons: Difference between revisions

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== Archimedean, uniform or semiregular tilings ==<!-- This section is linked from [[Archimedean tiling]] -->

{{Further|List of convex uniform tilings}}

[[Vertex-transitive|Vertex-transitivity]] means that for every pair of vertices there is a [[symmetry operation]] mapping the first vertex to the second.<ref name "Critchlow 1969">{{cite book |last1=Critchlow, p|first1=K. |title=Order in Space: A Design Source Book, |date=1969 |publisher=Thames and Hudson |___location=London |page=60- |pages=61}}</ref>

If the requirement of flag-transitivity is relaxed to one of vertex-transitivity, while the condition that the tiling is edge-to-edge is kept, there are eight additional tilings possible, known as ''Archimedean'', ''[[Uniform tiling|uniform]]'' or ''demiregular'' tilings. Note that there are two [[mirror image]] (enantiomorphic or [[Chirality (mathematics)|chiral]]) forms of 3⁴.6 (snub hexagonal) tiling, only one of which is shown in the following table. All other regular and semiregular tilings are achiral.