3D shapes and their properties

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Here are shadows of some 3D shapes. What shapes could have made them?