Why not make some polyhedra? You could make them from nets and cardboard, but why not be more daring and try using some other materials, perhaps as a cross-curricular project with your Art or Design & Technology department?
On these geometry pages are loads of ideas for investigating polyhedra, using a range of materials. Just have a look around and if you see something interesting, why not make it?
Investigate different polyhedra. How many vertices, edges and faces do they have?
What angles do they have?
Why are there only 5 regular polyhedra? An outline of a proof is here, although the diagram on the right gives a nice simple proof (taken from the qedcat website).
How many colours do you need to colour the faces of the regular polyhedra so that no faces of the same colour meet at an edge?
Why not investigate duality or vertex figures?
Perhaps you could investigate semi-regular polyhedra, or some more interesting ones?
Or perhaps you might want to investigate Schlafli symbols or Schlegel diagrams for polyhedra, and compare them with Planar graphs?
Tessellations are just flat polyhedra and are just as fun to explore!
You might find using zometools very useful for investigating polyhedra...
...and what better than to use the models for making bubbles when you've finished!?
Making polyhedra is a great opportunity for some origami! An amazing book is Unit Origami by Tomoko Fuse.
Modular origami is a great way of getting students to work together to create something amazing - click on the picture on the right to watch a VIDEO we made of an origami day we held at school.
And have a look here at my year 7 students making some rhombic dodedahedra!
...and origami gives you something nice to hang from the ceiling! Here is a picture of my classroom with Sonobe cubes my year 10 class made.
If you look very carefully, there is a stellated icosahedron in the background made by one of my year 13 students.
And here are some other nice shapes I made :)