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This football is a sphere and is therefore NOT a polyhedron.

Level 5-6 Shapes - Polyhedra

Polyhedra are 3D shapes with flat faces and straight edges. Explore prisms, pyramids and solids, count faces, edges and vertices, and meet Euler’s rule in KS3 Maths.

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Fascinating Fact:

Crystals often form natural polyhedra, like quartz with hexagonal prisms and diamond with cubic symmetry.

In KS3 Maths, you study polyhedra by examining faces, edges and vertices. You’ll classify prisms and pyramids, sketch nets, and use Euler’s formula to check your counts for common 3D solids.

Key Terms

Face: A flat 2D surface on a 3D shape.
Edge: A straight line where two faces meet.
Vertex (plural: vertices): A point where edges meet.

Frequently Asked Questions (Click to see answers)

What is a polyhedron in KS3 Maths?

A polyhedron is a 3D shape made only of flat polygon faces, straight edges, and vertices. Examples include cubes, prisms, and pyramids—not spheres or cylinders.

What is Euler’s formula for 3D shapes?

For convex polyhedra, Euler’s formula is V − E + F = 2, where V is vertices, E edges, and F faces. For a cube: 8 − 12 + 6 = 2.

What’s the difference between a prism and a pyramid?

A prism has two parallel, congruent polygon bases and rectangular side faces; a pyramid has one polygon base and triangular faces meeting at a single vertex.

Try These Related Quizzes

1 .

Which of these shapes is not a polyhedron?

Cube

Pyramid

Sphere

Triangular prism

Polyhedra have straight edges and flat surfaces

2 .

The polygons forming the surface of a polyhedron are called .......

areas

edges

faces

sides

Think of the 6 faces on a die which each show a different number

3 .

Where the straight sides of two polygons meet on the surface of a polyhedron they form a(n) .......

area

edge

line

side

A cube, like a die, has 12 edges

4 .

The place on the surface of a polygon where several edges meet is called a .......

corner

dent

point

vertex

Vertices are where the corners of 2-D shapes in a polyhedron meet

5 .

What is the name of the regular polyhedron in which four equilateral triangles meet at each vertex?

Hexahedron

Icosahedron

Octahedron

Tetrahedron

Imagine two square-based pyramids stuck together

6 .

If you add the number of faces of a polyhedron to the number of its vertices the result is always .......

equal to the number of edges

2 more than the number of edges

2 less than the number of edges

1 more than the number of edges

V + F = E + 2 is a formula discovered by the Swiss mathematician Leonhard Euler

7 .

How many edges has a pyramid with a hexagonal base?

Use Euler's formula with F = 7 and V = 7

8 .

How many faces has the regular polyhedron made with pentagons?

This is called a dodecahedron

9 .

A polyhedron with four rectangles or squares meeting at each vertex is called .......

a cuboid

a parallelepiped

a trapezoid

impossible

When four right angles meet at a point they completely fill the flat space so they cannot be folded into a solid

10 .

A polyhedron formed from rectangles set at right-angles to a polygonal base and top is called a .......

parallel

prism

prune

pyramid

The cross section of a prism is the same shape and size along its whole length

You can find more about this topic by visiting BBC Bitesize - 3D Shapes

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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