Please can someone tell me whether anyone has managed to classify all possible 3-D shapes into a finite and usefully small number of categories? At school level, most shapes seem to be some part, or combination, of:
There are too many impracticalities with what you are trying to do. 3d shapes can be made infinitely complex. You can classify vertices though, using the number of planes that are used construct them as your reference. A cube and rectangular prism alike could then be represented as figures consisting of eight 3-planes vertices, with say the notation 8*(90, 90, 90) to specify the angles that each of the planes represent. Of course, it's not as simple as that when it comes to complicated shapes - the different possible arrangements of the vertices in 3d space have to be taken into account.