30-degree tiling with an infinite set of pieces

The following transform shows how an infinite set of 30-degree pieces can be used to create a design.

The first diagram shows the transformation of triangles. Each triangle is transformed into a design that uses larger triangles. Thus, as the design grows, the triangle gets larger and larger.

The diagram also shows how the edges of the triangles are recursively developed. It is important that the edge of the larger triangle matches with other pieces, including multiple smaller pieces. The transform of the larger triangle has an edge made of diamonds and smaller triangles. This edge is created from two edges of the smaller triangle, plus a larger set of the same diamonds and squares of the smaller triangle.

The second diagram shows the transformation of the stars and diamonds. It also shows how the edge of the triangle is truncated and combined to create the edges of the stars and diamonds.

The following shows the diamonds D0 to D3 and larger diamonds D20 and D21.

PDF version (54 KB)

 

The following shows the triangles T0 to T3, T20 to T22, T40 to T42, and T80 and T81. The next shows T23. The last is T4.

PDF version (101 KB)

 

PDF version (157 KB)

 

PDF version (552 KB)

 

The following shows stars St0 to St2, St20 to St22, and St40 and St41. The next is St3.

PDF version (35 KB)

 

PDF version (81 KB)

 

Next shows how diamonds and triangles combine to form a dodecagon wheel. The following shows W0 to W2.

PDF version (83 KB)

 

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Copyright 1998-2004 by Jim Millar