The following transformation shows how 20-degree pieces can be used to create another version of the 30-degree tiling.

The 30 degree tiling has one diamond, one Y shape, and one triangle. This design has changed the diamonds to be a little fatter and a little thinner than the normal 30 degree diamond. Likewise, the Y shapes are fatter and thinner than the original Y shape.

The 30 degree tiling has one triangle. Above shows 2 triangles, and the transforms show they transform to different diamonds and Ys from each other.

The mapping of the thin diamond D_{0} to the green triangle D_{1} and the fat
diamond D_{0} to the blue triangle D_{1} is somewhat arbitrary. If this mapping were
reversed, interestingly the same diamonds D_{2} emerge from the design.

This tiling demonstrates that the 30 degree tiling is not a rigid structure, but has some freedom in the angles in the design even when all the sides are held rigid.

The following shows the diamonds D_{0} to D_{4}.

PDF version (22 KB) |

The following shows the triangles T_{0} to T_{4}.

PDF version (21 KB) |

The following shows the Y shapes Y_{0} to Y_{4}.

PDF version (31 KB) |

The following shows the wheel that emerges at every vertex as the
design grows, W_{0} to W_{4}.

PDF version (140 KB) |

Back to ideas for more designs.

*Copyright 1998-2004 by Jim
Millar *