3D shapes and their properties

What is the shape of wrapping paper that you would need to completely wrap this model?

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.

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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

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?

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.

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