1. Symmetries of Solids

2. Reflectional Symmetry
Consider the solid as shown.
If there is a plane that can divide the solid into two halves
which are mirror images of each other ,
then the solid is said to have reflectional symmetry.
plane of reflection
The plane that divides the solid is called the plane of reflection.

3. For example, a cuboid with square base has 5 planes of reflection as shown below:

4. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line,
Consider the solid as shown. X Y A B C D

5. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line, X Y B A C D

6. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line, X Y
180 C B D A
repeat the 1st time

7. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line, X Y D C A B

8. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line, X Y A B C D
repeat the 2nd time

9. Rotational Symmetry
If the solid repeats itself more than once after making one complete revolution about a straight line,
it is said to have rotational symmetry. X Y A B C D
axis of rotational symmetry
The straight line is called the axis of rotational symmetry.

10. We say that the cuboid is a solid with 2-fold rotational symmetry and X Y A B C D
axis of 2-fold
rotational symmetry
In the above figure, after the cuboid makes one complete revolution about the straight line XY, it repeats twice.
We say that the cuboid is a solid with 2-fold rotational symmetry and
the line XY is called the axis of 2-fold rotational symmetry of the cuboid.

11. A solid may have more than one axis of rotational symmetry.
Consider the following cuboid with square base.
axis of 4-fold
rotational symmetry
axis of 2-fold
rotational symmetry

12. How many planes of reflection are there in a prism with isosceles trapezium as its base?
There are 2 planes of reflection.

13. How many axes of rotational symmetry are there in a prism with isosceles trapezium as its base?
There is 1 axis of 2-fold rotational symmetry.