30-degree tiling

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 D0 to the green triangle D1 and the fat diamond D0 to the blue triangle D1 is somewhat arbitrary. If this mapping were reversed, interestingly the same diamonds D2 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 D0 to D4.

PDF version (22 KB)

The following shows the triangles T0 to T4.

PDF version (21 KB)

The following shows the Y shapes Y0 to Y4.

PDF version (31 KB)

 The following shows the wheel that emerges at every vertex as the design grows, W0 to W4.

PDF version (140 KB)

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Copyright 1998-2004 by Jim Millar