Escher-Like Tessellations Explorations

Objective: Escher developed his tessellations from the more primitive geometric tessellations using isometries. We will practice several of the techniques that will create an Escher-like tessellation.

This exploration is aimed at using the techniques from the first section of Tessellations by Recognizable Figures to create some tessellations

1. Use translations to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. Make sure you create a tessellation with a recognizable figure!

4. Find the midpoints on the sides of one of the following hexagons, modify half of each of the sides, and propagate this change by 180° rotations through the midpoints. Make sure you create a tessellation with a recognizable figure!

Handin: A sheet with answers to all questions.