Page 140 - ICSE Math 5

Symmetry in 3D Shapes or Solids

We have studied about symmetry in 2D or two-dimensional shapes or figures where the line
of symmetry plays the role of a mirror. However, 3D or three-dimensional figures or solids also
show symmetry.

A plane that divides a 3D figure or solid into two identical halves or mirror images is called a
plane of symmetry. If a 3D figure is cut into two halves with a two-dimensional plane and the cut
surfaces are placed in front of a mirror, then each half of the figure will be the mirror image of
the other.

As 2D figures have one, two or more lines of symmetry, 3D figures or solids can also have more
than one plane of symmetry.

Symmetry in Geometrical Shapes

Let’s consider an example of a cube to understand symmetry in 3D shapes.
A cube has 9 planes of symmetry as shown below. Each plane of symmetry divides the cube into
two identical halves.

Let’s see a cuboid now. It has 3 planes of symmetry.

A sphere and a cone have infinite number of planes of symmetry.

Symmetry in Human Body and Animals

Human body also shows a type of symmetry called bilateral symmetry
or mirror symmetry. It is also called plane symmetry.

In this type of symmetry, a human body can be divided vertically into
two equal halves by drawing an imaginary line down the centre. The
left and right halves of the body exhibit mirror images of each other.

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