A geometric proof of the Kochen-Specker no-go theorem

We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).