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We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Platonic Planet

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

Face Painting

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Cubic Conundrum

Age 7 to 16
Challenge Level

Students could be challenged to visualise how the different cubes could be constructed from the net.

Perhaps working in pairs, students could try to convince each other why (and how) certain cubes can be made, and why certain cubes cannot be made.

Copies of the printed sheets, scissors and sticky tape could be made available at a later stage to allow students to cut up the net and make the various cubes to check their predictions.

The second part of the problem could be tackled in a similar way.