Fold an ancient Chinese dice

Thousands of years ago, ancient Chinese people played a game with strange dice – and now you can make your own!

You will need

Someone is cutting out a complicated shape.

What to do

Cut out the shape – known as the net – along the outermost lines.
Fold and then unfold along each of the lines on the net. They all fold in the same direction, so you don’t need to turn the paper over.
Before you start taping, try and form the shape of the dice.

Before you start taping, try to form the shape you’re making. There are a few rules to this shape:

Faces only meet at edges, they don’t overlap.
The paper only needs to bend on the lines.
Squares only share edges with hexagons, never with squares.

Once you’re happy with the shape of your dice, use small pieces of sticky tape to stick adjacent sides together. For a cleaner look, you can put the sticky tape on the inside of the dice, rather than the outside.
Tape the shapes together – squares to hexagons.

When you’re finished, you can write numbers on it. The ancient Chinese wrote the numbers 0–6 on the dice, writing each number on two different sides. You can do this too, or you can use your own numbering scheme!

What’s happening?

This shape is known as a truncated octahedron. It is quite similar to an eight sided dice shape known as an octahedron. To turn an octahedron into a truncated octahedron, cut the corners off to reveal six square sides.

The completed dice shape - with hexagon and square faces.

You can also make this shape starting with a cube. If you cut a small amount off each of the corners of a cube, you get a shape called a truncated cube. This has eight triangular faces, and six octagonal ones. Cut a bit deeper and you get a cubeoctahedron, with triangle and square faces. Cut even deeper and you get the truncated octahedron shape of this dice.

The hexagons and squares of this dice have roughly the same area. But that doesn’t mean they roll with exactly the same probability. Can you come up with an experiment to test whether this dice is fair?