45-degree tiling

The following set of pieces show how a 45-degree tiling can be created using 30-degree pattern blocks.

The 45 degree tiling has on diamond, on square, and one X shaped piece. This design has changed the diamonds to a fatter and a thinner diamond than the normal 45 degree diamond. Likewise, the X shaped pieces are fatter and thinner than the original X shaped pieces.

The 45 degree tiling has one square. The transform above shows two squares, transforming to different Xs and diamonds.

The mapping of the thin diamond D0 to D1 and the fat diamond D0 to D1 is somewhat arbitrary. If this mapping were switched, interestingly the same diamonds D2 emerge from the design.

This tiling demonstrates that the 45 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 diamonds D0 to D4.

PDF version (17 KB)

 

The following shows the squares S0 to S4.

PDF version (22 KB)

 

The following shows the X shaped pieces X0 to X4.

PDF version (31 KB)

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

PDF version (81 KB)

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Copyright 1998-2004 by Jim Millar