File:Regular polygons meeting at vertex 5 3 3 3 4 4.svg

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English: This image illustrates an example of Combinations of regular polygons that can meet at a vertex.

For Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees. There are seventeen combinations of regular polygons whose internal angles add up to 360 degrees, each being referred to as a species of vertex; in four cases there are two distinct cyclic orders of the polygons, yielding twenty-one types of vertex. Only eleven of these can occur in a uniform tiling of regular polygons. In particular, if three polygons meet at a vertex and one has an odd number of sides, the other two polygons must be the same. If they are not, they would have to alternate around the first polygon, which is impossible if its number of sides is odd. These arrangements are here enumerated:

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Date/TimeThumbnailDimensionsUserComment
current21:08, 16 June 2015Thumbnail for version as of 21:08, 16 June 2015120 × 113 (585 bytes)Dllu (talk | contribs)use stroke-linejoin: round; and use style tag to reduce filesize
21:22, 1 June 2013Thumbnail for version as of 21:22, 1 June 2013120 × 113 (605 bytes)Dllu (talk | contribs)User created page with UploadWizard

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