Here are Plato's two perfect triangles from his seminal work "Timaeus" that can create the 5 platonic solids (which are according to him form the elements of earth, air, water, fire ...)

They are worth having as objects in the bookshelf to use and demonstrate how to build platonic solids, geodesic domes, tensegrity structures, etc.  Also they can be used to for statics class to demonstrate simple trigonometry (45/45/90 and 30/60/90 triangles), as well as x and y components of force vectors in statics.