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

Dodecamagic

Age

7 to 11

Challenge level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
problem

Child's Play

Age

7 to 11

Challenge level

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
problem

A Chain of Eight Polyhedra

Age

7 to 11

Challenge level

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?
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

Redblue

Age

7 to 11

Challenge level

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
problem

Icosian Game

Age

11 to 14

Challenge level

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
problem

Classifying Solids Using Angle Deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem

Dodecawhat

Age

14 to 16

Challenge level

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
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.