Polyhedron consisting of equilateral triangles. The number of faces (F) a convex deltahedron can have is limited to 4<F<20 - it is impossible to create a 3D shape with less triangles than the tetrahedron, and the maximum number of equilateral triangles you can join at a single vertex is five, resulting in a 20-sided icosahedron.
Also, any deltahedron is limited to an even number of faces since a deltahedron with E edges and F faces follows the equation E=(3/2)F. So F must be even, as E is an integer.
To derive the equation, imagine a pile of loose triangles, before they are joined together. As each triangle has three sides, there are three times as many triangle-edges as triangles. When we join the triangles together, two triangle-edges become one polyhedron edge, giving E=(3/2)F.
No upper limit on the number of faces exist for non-convex polyhedra; any single triangle might be replaced with a 'dimple' or 'bump' consisting of three triangles (note the opportunity for Kochian recursion!), and every pentagon might be replaced with a dimple of five triangles.