The symmetry properties of the plane figure formed by the fo

The symmetry properties of the plane figure formed by the four points at the corners of a rectangle (not a square) can be described in terms of four symmetry operations: the identity operation and three rotations. (i) Describe these symmetry operations. (ii) Construct the group multiplication table

Solution

Solution:

AS given the symmetry elements of the rectangle can be chosen as the three 2-fold axes of rotation:

Oz, Ox, Oy (an alternative choice is the axis Oz and the bisecting planes xz and yz).

Let\'s first Describe the symmetry operations

(i) Describe these symmetry operations.

The symmetry operations are as follows:

E the identity operation that leaves every point unmoved

A rotation through 180° about the Oz-axis

B rotation through 180° about the Ox-axis

C rotation through 180° about the Oy-axis

(ii) Construct the group multiplication table