Solid shapes --- cube --- tetrahedron --- octahedron --- icosahedron --- dodecahedron --- other shapes --- Euler's formula --- glossary --- for teachers

Description of an icosahedron

A tetrahedron is made of triangles with three triangles at each point. An octahedron has four triangles at each point. Can we fit five triangles at each point? Yes, we can, and it's called an icosahedron. It has 20 faces.

There are 43380 distinct nets for the icosahedron, so I don't expect you to find them all! An icosahedron can be thought of as ten triangles going round the 'equator', with five at the 'north pole' and five at the 'south pole'. Thinking of this helps us to work out a net.

Model of an icosahedron

This model (right) was made from a kit with magnetic connections. Since it just shows the edges, you can see through the model, which means that you can count the vertices and edges easier. Unfortunately, since the icosahedron is quite complicated, one edge and one vertex(corner) is hidden, several more are hard to make out, and the shadows don't help! Still, you can guess, or perhaps you can make up your own model to count from. How many vertices (corners) and edges are there? See Euler's formula.

Net of an icosahedron

Here is one net for an icosahedron. Print it out, stick it on thin card, score along the lines and fold them, form the shape, then stick it together with small amounts of glue.

For more details, see the notes for the net of a cube.

Colour scheme for model

You might like to think of a colour scheme for your finished shape. It's a lot easier if you colour it in before you stick it together, or even before you cut it out. Try to imagine what the finished shape will look like when colouring it in. You could try to draw lines that run over edges. That's easy if the faces are together in the net, less easy if there are gaps! Do you want straight lines or curvy ones? Can you draw a line which will end up going right round the shape? How about colouring all the bits near a point in the same colour? You could paint the 'equator' one colour, and the two 'poles' another. There are diamonds on the finished surface - try finding them and painting them. An icosahedron is fairly close to a sphere, so if you are really ambitious, you could try drawing the world on it.

Then when you stick it together, you can see if your shape's design looks anything like you imagined it would!

Common cold virus


Many viruses have the shape of an icosahedron. This is a common cold virus, with the icosahedron drawn on.

Moving icosahedron

Click on Move or Backwards to make tetrahedron move and Stop to stop it.

Other regular solids with triangular faces?

So far, we have found a tetrahedron with three triangles at each vertex (corner), an octahedron with four triangles and an icosahedron with five triangles. If you try to fit six triangles round a point, it becomes flat, so there are no more.