Polyhedra

problem
Face painting

Age

7 to 11

Challenge level

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.
problem
Tetrahedron faces

Age

7 to 11

Challenge level

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
problem
Tetra inequalities

Age

16 to 18

Challenge level

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?
problem
Reach for polydron

Age

16 to 18

Challenge level

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.
problem
Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?
problem
Platonic planet

Age

14 to 16

Challenge level

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?
problem
Proximity

Age

14 to 16

Challenge level

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
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Platonic and Archimedean solids

In a recent workshop, students made these solids. Can you think of reasons why I might have grouped the solids in the way I have before taking the pictures?
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Making maths: triangular ball

Make a ball from triangles!