Chapter 14.8, Problem 4E

To determine

To make a table of three symmetries of the figure.

Answer to Problem 4E

The table of symmetry is

$°$	I $R_{0,}$ ${}_{90}$ $R_{0,}$ ${}_{180}$ $R_{0,}$ ${}_{270}$
I $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$	I $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{120}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{90}$ $R_{0,}$ ${}_{270}$

Explanation of Solution

Given information:

The given statement is make a table of three symmetries of the figure.

Assume $R_0$ be the rotation around O in the figure.

The table of symmetry is

$°$	I $R_{0,}$ ${}_{90}$ $R_{0,}$ ${}_{180}$ $R_{0,}$ ${}_{270}$
I $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$	I $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ $R_0$ ${}_{90}$ $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{180}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{120}$ $R_0$ ${}_{270}$ I $R_0$ ${}_{90}$ $R_{0,}$ ${}_{270}$