Triangular tiling: Difference between revisions

Revision as of 10:34, 1 August 2015

Revision as of 00:30, 2 August 2015

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== Uniform colorings ==

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 and 111112 areis reduced from 121314.<ref>Tilings and Patterns, p.102-107</ref>

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

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|BGCOLOR="#ffc0c0"|121213

|BGCOLOR="#c0ffc0"|111212

|BGCOLOR="#c0ffc0"|111112

|BGCOLOR="#ffc0c0"|121314

|BGCOLOR="#c0ffc0"|111213

|BGCOLOR="#c0ffc0"|111112

|-

|[[File:Uniform_triangular_tiling_121213.png|75px]]

|[[File:Uniform triangular tiling 111212.png|75px]]

|[[File:Uniform triangular tiling 111112.png|75px]]

|[[File:Uniform_triangular_tiling_121314.png|75px]]

|[[File:Uniform triangular tiling 111213.png|75px]]

|[[File:Uniform triangular tiling 111112.png|75px]]

|- align=center

|colspan=2|p3m1 (*333)

|colspan=32|p3p31m (3333*3)

|colspan=2|p3 (333)

|}