Triangular tiling: Difference between revisions

Revision as of 21:30, 2 August 2015

Revision as of 21:49, 2 August 2015

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There are 9 distinct [[uniform coloring]]s of a triangular tiling. (Naming the colors by indices on the 6 triangles around a vertex: 111111, 111112, 111212, 111213, 111222, 112122, 121212, 121213, 121314) Three of them can be derived from others by repeating colors: 111212 and 111112 from 121213 by combining 1 and 3, while 111213 is reduced from 121314.<ref>Tilings and Patterns, p.102-107</ref>

There is one class of [[Archimedean coloring]]s, 111112, (marked with a *) which is not 1-uniform, containing alternate rows of triangles where every third is colored. The example givenshown is 2-uniform, but there are infinitely many such Archimedean colorings that can be created by arbitrary horizontal shifts of the rows.

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