File:Regular polygons meeting at vertex 5 3 3 3 3 6.svg

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Description	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: 3 polygons of sides 3 7 42 3 polygons of sides 3 8 24 3 polygons of sides 3 9 18 3 polygons of sides 3 10 15 3 polygons of sides 3 12 12 3 polygons of sides 4 5 20 3 polygons of sides 4 6 12 3 polygons of sides 4 8 8 3 polygons of sides 5 5 10 3 polygons of sides 6 6 6 4 polygons of sides 3 3 4 12 4 polygons of sides 3 4 3 12 4 polygons of sides 3 3 6 6 4 polygons of sides 3 6 3 6 4 polygons of sides 4 4 4 4 4 polygons of sides 3 4 4 6 4 polygons of sides 3 4 6 4 5 polygons of sides 3 3 3 3 6 5 polygons of sides 3 3 3 4 4 5 polygons of sides 3 3 4 3 4 6 polygons of sides 3 3 3 3 3 3
Date	1 June 2013, 14:17:54
Source	Own work
Author	Dllu

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	22:09, 16 June 2015		145 × 150 (653 bytes)	wikimediacommons>Dllu	use stroke-linejoin: round; and use style tag to reduce filesize

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