When you connect the center of each triangle across the common sides of the tessellating

Chapter 7, Problem 9

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When you connect the center of each triangle across the common sides of the tessellating equilateral triangles at right, you get another tessellation. This new tessellation is called the dual of the original tessellation. Notice the dual of the equilateral triangle tessellation is the regular hexagon tessellation. Every regular tessellation of regular polygons has a dual. a. Draw a regular square tessellation and make its dual. What is the dual? b. Draw a hexagon tessellation and make the dual of it. What is the dual? c. What do you notice about the duals?

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