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Some explanations of (3.6)^2 patterns consisting of 2 opposite equilateral triangles and 2 opposite regular hexagons had (3.6)^6 written, these have been corrected. |
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There are 17 combinations of regular convex polygons that form 21 types of [[Vertex (geometry)#Of a plane tiling|plane-vertex tilings]].<ref>{{citation|title=The Elements of Plane Practical Geometry, Etc|first=Elmslie William|last=Dallas|publisher=John W. Parker & Son|year=1855|page=134|url=https://books.google.com/books?id=y4BaAAAAcAAJ&pg=PA134}}</ref><ref>Tilings and Patterns, Figure 2.1.1, p.60</ref> Polygons in these meet at a point with no gap or overlap. Listing by their [[vertex figure]]s, one has 6 polygons, three have 5 polygons, seven have 4 polygons, and ten have 3 polygons.<ref>Tilings and Patterns, p.58-69</ref>
As detailed in the sections above, three of them can make [[#Regular_tilings|regular tilings]] (6<sup>3</sup>, 4<sup>4</sup>, 3<sup>6</sup>), and eight more can make [[#Archimedean,_uniform_or_semiregular_tilings|semiregular or archimedean tilings]], (3.12.12, 4.6.12, 4.8.8, (3.6)<sup>
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|valign=bottom|[[File:Regular polygons meeting at vertex 4 3 4 3 12.svg|40px]]<BR>3.4.3.12
|valign=bottom|[[File:Regular polygons meeting at vertex 4 3 3 6 6.svg|40px]]<BR>3.3.6.6
|valign=bottom|[[File:Regular polygons meeting at vertex 4 3 6 3 6.svg|40px]]<BR>(3.6)<sup>
|valign=bottom|[[File:Regular polygons meeting at vertex 4 3 4 4 6.svg|40px]]<BR>3.4.4.6
|valign=bottom|[[File:Regular polygons meeting at vertex 4 3 4 6 4.svg|40px]]<BR>3.4.6.4
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