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 D_{0} to D_{3} and larger
diamonds D2_{0} and D2_{1}.

PDF version (54 KB) |

The following shows the triangles T_{0} to T_{3}, T2_{0}
to T2_{2}, T4_{0} to T4_{2}, and T8_{0} and T8_{1}.
The next shows T2_{3}. The last is T_{4}.

PDF version (101 KB) |

PDF version (157 KB) |

PDF version (552 KB) |

The following shows stars St_{0} to St_{2}, St2_{0}
to St2_{2}, and St4_{0} and St4_{1}. The next is St_{3}.

PDF version (35 KB) |

PDF version (81 KB) |

Next shows how diamonds and triangles combine to form a dodecagon wheel. The
following shows W_{0} to W_{2}.

PDF version (83 KB) |

Back to ideas for more designs.

*Copyright 1998-2004 by Jim
Millar *