# Octahedron

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

### Description of an octahedron

A tetrahedron has three faces meeting at each point, similar to a cube. We saw that you cannot make a polyhedron with four squares meeting at each point, but you can do it with four triangles. This makes a shape called an octahedron. You can tell from its name that it has eight faces (similar to an octagon, which is a flat shape with eight angles).

### Model of an octahedron

This model (left) 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. How many vertices (corners) and edges are there? See Euler's formula. An octahedron can look different from different angles. It can look like two pyramids or, from the top, it can look like a star of David.

### Game with nets of cubes

See if you can find all the nets for an octahedron below. There are eleven correct nets, and they will change colour as you click on them. Click on New go for another go.

11 nets left to find

### Hints for game

Of course, for an octahedron, you must have eight triangles in the net. There are also four triangles round a point. These are hard to work out round the edge, but if five or six triangles are together, you know that something is wrong.

### Net of an octahedron

Here is one net for an octahedron. 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.

### Octahedral box

Octahedra are not usually used as packaging! But in fact an octahedron makes an attractive box. You usually think of an octahedron on its point, as this makes its shape obvious. However, if you lay it flat on one face, then it has not only a flat bottom but a flat top as well. However, the sides are not vertical. You need to think how to make it into a box with a lid. Perhaps you could make two octahedra, each with one side removed and one bigger than the other. Then the bigger one could fit over the smaller one. It must only be bigger by a very small amount, or it will rattle.

### Octahedral crystals

Octahedra happen in crystals as well as cubes. This is a natural spinel crystal. Spinels are red gem stones, often mistaken for rubies.

### Moving octahedron

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

### Other regular solids with triangular faces?

An octahedron has four triangles at each vertex (corner). It is possible to have a different number of triangles at the vertex of a regular solid. These make a tetrahedron or an icosahedron.