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Proximity

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

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?

Three Cubes

Can you work out the dimensions of the three cubes?

Dodecawhat

Age 14 to 16 Challenge Level:

Join AO in the first diagram. What is the angle between AO and the red fold line? Now find angle REO.