Clowns and other entertainers twist long slender balloons that into a great variety of animal and other shapes. The same balloons are ideal for creating polyhedra and other 3D structures - it's easy and fun to experiment with various constructions. But questions quickly arise. How many balloons do you need to make a dodecahedron (or any other shape)? What are practical procedures? What do these have to do with Euler's theorems? And how should we pronounce Euler anyway?