# 3D Symmetry

## 3D Symmetry Revision

**3D Symmetry**

Similarly to 2D shapes, some 3D shapes are also **symmetrical**. Rather than having lines of **symmetry**, 3D shapes have **planes** of** symmetry**. A plane of symmetry occurs if you can cut the shape into two halves, the halves are mirror images of each other.

We will look at the 3D **symmetry** of **cylinders**, **prisms**, and **pyramids**.

**Cylinders**

Cylinders have circular **symmetry**, meaning they have an **infinite number** of planes of **symmetry**.

They have one plane of **symmetry** across the curved face:

If the cylinder is cut in half at this plane of **symmetry**, it produces two shapes that are mirror images of eachother.

Cylinders have circular **symmetry** with planes of **symmetry** such as the following:

These planes of **symmetry** can be infinitely rotated, giving an infinite number of planes of **symmetry**.

**Prisms**

Regular triangular prisms have 4 planes of **symmetry**.

They have one plane of **symmetry** across the rectangular face:

And they have 3 planes of **symmetry** as following:

This plane of **symmetry** can be from any of the 3 vertices, giving the shape a total of 4 planes of **symmetry**.

For other prisms, it is useful to draw or visualise the shape and identify the planes of **symmetry**.

**Pyramids**

Square based pyramids have 4 planes of **symmetry**, as shown below:

Regular triangular based pyramids have up to 6 planes of **symmetry**, as shown below:

## 3D Symmetry Example Questions

**Question 1:** State the number of planes of symmetry in an isosceles triangular prism.

**[2 marks]**

**Question 2:** State the number of planes of symmetry in a sphere.

**[2 marks]**

A sphere contains infinitely many planes of symmetry.

**Question 3:** State the number of planes of symmetry in a rectangular-based pyramid.

**[2 marks]**