Below are some images of a dodecahedron I built using a technique called tensegrity.  

It is very cheap to make - I used straws (thanks Starbucks), rubber bands and paper clips.  You don't even need glue! 

The instructions (follow the link above) are very clear, but make sure you are consistent and careful when attaching the rubber bands otherwise it won't work! Also, they shouldn't be so tight that it is a struggle to put the them on. 

I am not sure if I would attempt this in a classroom as it is quite difficult to make, but it could be good for G&T students as part of a project maybe?  
Or maybe just make it for fun?