So here they are. They’re built. In Ancient Greek elemental theory, the cube represented Earth; the tetrahedron represented Fire. The dodecagon was Universe. The icosahedron was Water. The octahedron was Air.
Mathematically, a cube has six sides (the Doctor says "seven — including the INSide"). The tetrahedron has 4 (five, says Doctor Who). The dodecagon has 12 (13!). The icosahedron has 20 (21! Why must I keep saying this??), and the octahedron has eight ("nine! Nine sides muhahahahahaha… Oh, wait… Wrong tv personality.")
Hot geometry in planar solids.