nerd time

i might be the least science and math-oriented person i know, but for some reason i'm really into the platonic solids -- convex polyhedra with regular polygon faces, in which all sides and angles are identical. there are only five: the tetrahedron (4 faces of equilateral triangles), the hexahedron (or cube), the octahedron (8 faces of equilateral triangles), the dodecahedron (12 faces of hexagons), and the icosahedron (20 faces of equilateral triangles). here's how we know that there are only five:

There have to be at least three polygons at a vertex; two would simply fold together back to back. Also the angles around a vertex cannot exceed 360 degrees, and if they equal 360 degrees, the polygons simply tile the plane. Thus we can rule out solids with 6 or more faces - hexagons tile the plane and all other triplets exceed 360 degrees. That means convex solids with regular polygon faces can only have triangles, squares or pentagons as faces. The only possibilities are 3, 4, or 5 triangles, 3 squares or 3 pentagons (at a vertex). Thus there are only five platonic solids.

so it's perfectly logical that there are only five platonic solids, but they seem magical to me. the ancient greeks were into them too, and so are many other nerd nut jobs. plus they can all be folded from a single piece of paper, which you know is kinda neat.