Chapter 14.8, Problem 3E

To determine

To make a table of three symmetries of the figure.

Answer to Problem 3E

The table of symmetry is

$°$	I $R_{0,}$ ${}_{120}$$R_{0,}$ ${}_{240}$
I  $R_0$ ${}_{120}$ $R_0$ ${}_{240}$	I $R_0$ ${}_{120}$ $R_0$ ${}_{240}$ $R_0$ ${}_{120}$ $R_0$ ${}_{240}$ I   $R_0$ ${}_{240}$ I $R_0$ ${}_{120}$

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. And I is the identity symmetry.

The table of symmetry is

$°$	I $R_{0,}$ ${}_{120}$$R_{0,}$ ${}_{240}$
I  $R_0$ ${}_{120}$ $R_0$ ${}_{240}$	I $R_0$ ${}_{120}$ $R_0$ ${}_{240}$ $R_0$ ${}_{120}$ $R_0$ ${}_{240}$ I   $R_0$ ${}_{240}$ I $R_0$ ${}_{120}$