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