Platonic solids are very unique shapes. From all possible convex polyhedra, only five can be made with regular polygons as faces. There are many ways to prove there can't be a sixth Platonic solid, one of them is trying it yourself!
Platonic Solids can be combined in many different ways. They are commonly connected by the corners (vertex), edges or just stacked. Be creative and avoid solutions that fold or damage the straws, they are reusable.