Symmetries of Solids.

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Presentation transcript:

Symmetries of Solids

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.

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

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

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

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

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

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

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.

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.

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

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

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.