[M.D. Holloway]

We did the same thing in 7th grade - we couldn't use glue or gussets. The fact that you can is going to make it easy. The strength you can garner from the gussets and glue will easily allow for structural intergity to be relized.

Go with the Tetrahedron structure, double wall the strews like kach22i et al suggested. If cutting the straws is allowed, split them in order to have 3 connevting at the gussets. I would use a stiff cyano-gel glue and thick cardstock (or use a glue gun!). Corregated may work as well, the strength to weight ratio makes sense in 2 of the 3 planes - if weight is not important do the cardstock. Stay away from the polystyrene foam board, the glue will melt it.