3D shapes and their properties

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.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Can you make a 3x3 cube with these shapes made from small cubes?

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.

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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?

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?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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?