The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

How can you determine if a tiling of the plane is semiregular? pg. 69 Which irregular n-gons always tile the plane? pg. 74

Reference:

A semiregular tiling is an edge-to-edge tiling by two or more different types of regular polygonal regions in which vertex figures are the same size and shape no matter where they are drawn in the tiling.

Tilings Involving n-gons for n ≥ 7 The problem of tiling the plane with 7-gons, 8-gons, or other n-gons, with n ≥ 7, is perhaps the most interesting of all. It was proved by K. Reinhardt in 1927 that no convex polygon with more than six sides can tile the plane!

The results of our investigation of tilings are summarized in Table 2.4.