i have built many polyhedra and two schemes standout:
1) best is celluose acetate sheets glued by bonding edges with acetone. (you must ventilate the work area.) the acetate sheets are easily scored with a scribe and then snapped. these models are reasonably robust and transparent; this latter can be very effective with a viewgraph machine -- changing the focal plane brings different shapes into focus.
2) easiest is with polydron pieces. these ar enot real cheap but are indestructible and a lot of fun. i have a set of models in my office and everyone who comes in plays with them.
a good reference book for fun stuff is bonnie stewart's ``adventures amongst the toroids'' -- a weird and beautiful collection of polyhedra with tunnels (topologically equivalent to a torus (or many looped torus)) constructed with regular polygons.