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

The 30 degree tiling has one diamond, 3 triangles, and two squares. This design has changed the diamonds to be a little fatter and a little thinner than the normal 30 degree diamond.

Likewise, the squares are fatter and thinner than the original squares.

Finally the yellow triangle became a yellow and a blue triangle.

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_{3}.

PDF version (28 KB) |

The following shows the green and purple triangles GT_{0} to GT_{3
}and PT_{0} to PT_{3}.

PDF version (45 KB) |

The following shows the yellow and blue triangles YT_{0} to YT_{3
}and BT_{0} to BT_{3}.

PDF version (46 KB) |

The following shows the red, pink, and orange squares RS_{0} to RS_{3},
PS_{0} to PS_{3} and OS_{0} to OS_{3}.

PDF version (66 KB) |

The following shows the wheel that emerges at every vertex as the
design grows, W_{0} to W_{3}.

PDF version (206 KB) |

Back to ideas for more designs.

*Copyright 1998-2004 by Jim
Millar *