7.4 Tessellations with Regular Polygons

EXERCISES
1. Sketch two objects or designs you see every day that are monohedral
tessellations.
2. List two objects or designs outside your classroom that are semiregular tessellations.
In Exercises 3–5, write the vertex arrangement for each semiregular tessellation
in numbers.
3. 4. 5.
In Exercises 6–8, write the vertex arrangement for each 2-uniform tessellation
in numbers.
6. 7. 8.
9. 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?
10. You can make dual tessellations of semiregular tessellations, but they
may not be tessellations of regular polygons. Try it. Sketch the dual of
the 4.8.8 tessellation, shown at right. Describe the dual.
Technology In Exercises 11–14, use geometry software, templates of regular
polygons, or pattern blocks.
11. Sketch and color the 3.6.3.6 tessellation. Continue it to fill an entire
sheet of paper.
12. Sketch the 4.6.12 tessellation. Color it so it has reflectional symmetry but not
rotational symmetry.
392 CHAPTER 7 Transformations and Tessellations
You will need
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