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

# Level 5-6 Shapes - Polyhedra

So, you are studying shapes in KS3 Maths. By now you'll be all to familiar with 2-Dimensional shapes like triangles, oblongs, trapeziums, octagons and the like. But what about 3-Dimensional shapes like cubes or pyramids? These are called polyhedrons or polyhedral.

Any solid, 3-Dimensional shape made by fitting polygons together is called a polyhedron. A regular polyhedron is formed from regular polygons all the same size and shape, for example a cube or a dodecahedron. Irregular polyhedrons are made up of different shapes, for example a typical prism is made from triangles and rectangles. There are certain characteristics that polyhedrons have which 2-D shapes don't - faces, edges (where 2 faces meet) and vertices (where corners meet).

To find out how well you know your polyhedrons, try this quiz. And don't forget the helpful comments which appear after each question. These often help to clear up anything you weren't sure of.

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?
6
8
10
12
Use Euler's formula with F = 7 and V = 7
8.
How many faces has the regular polyhedron made with pentagons?
5
10
12
15
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
Author:  Frank Evans