The ancient Greek mathematician Euclid proved in his Elements of Geometry that there are only five Platonic solids – the regular tetrahedron (four sides that are equilateral triangles), the cube (six ...

four make an octahedron and five make an icosahedron. Six triangles make a flat sheet that can't be folded into a corner. So only three Platonic solids can be made from triangles. Image caption ...