Escher-Like Tessellations Explorations

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Time-45.svg

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 as described above 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!

Parallellogram-net.png

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!

Diamond-net.png

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!

Square-net.png


4. Find the midpoints on one of the following squares, 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!

Hexagon-net.png


Handin: A sheet with answers to all questions.