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Irregular Tiling

Midpoint Rotation. Start with any tiling using quadrilaterals or triangles. (Note: we can tile a plane with any of these.)Pick a side and find its midpoint.Given any shape on one side of the midpoint, rotate it through 180 degrees to form the other side.. Escher Example. Side Rotation. Start with any regular tiling.Cut out a shape on one side, rotate it to an adjacent side using the endpoint..

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Irregular Tiling

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    1. Irregular Tiling Our goal: find ways to generate irregular tilings from regular or simple irregular tilings Methods so far: parallel translation glide reflection

    3. Escher Example

    4. Side Rotation Start with any regular tiling. Cut out a shape on one side, rotate it to an adjacent side using the endpoint.

    5. Escher Example

    6. Practice Using the triangular grid paper create an irregular tiling using midpoint rotation on one side of an equilateral triangle create an irregular tiling using side rotation on a hexgon Given the patterns, try to identify which method from today was used to create it.

    7. Conway Criterion A loop without crossing and punctures will tile the plane if you can divide it into 6 arcs with endpoints A, B, C, D, E, and F where the arc AB is the parallel translate of ED arcs BC, CD, EF, and FA have rotational symmetry about their midpoints

    8. Example Explain why the below shape fits the Conway Criterion. Check out more examples at http://www.mpls.k12.mn.us/~rrumppe/ConTess.html

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