Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative relations among angles and length ratios pertaining to planes and lines as solid boundaries and the relations of these to planes and axes of symmetry. Simple but general and far-reaching notions of symmetry in analysis are mentioned. (Contains 2 figures.)