 # Platonic Solids

A "polygon" is a figure on a plane (2-dimensional — like a piece of paper) where all the sides are straight lines, and the lines connect to form a closed region. Here are a few polygons: A "regular polygon" is a polygon where all the sides have the same length, and all the interior angles (the angles on the inside) are the same. Here are some regular polygons: It turns out that if you want to make a 3-dimensional figure out of nothing but regular polygons (where all the angles on the outside are convex/greater than 180°) there are only five ways to do it. This was known in ancient times, and although we're sure Plato himself didn't figure this out, he did discuss this at length.

See the Wikipedia article on Platonic Solids.

### The Five Platonic Solids

• Face: a two-dimensional regular polygon
• Edge: a one-dimensional line joining to faces
• Vertex: a point joining two edges

(Images courtesy of Wikipedia)
Polyhedron Vertices Edges Faces
Tetrahedron
πυραμιδος 4 6 4
Cube
κυβος 8 12 6
Octahedron
οκταεδρος 6 12 8
Dodecahedron
δωδεκαεδρος 20 30 12

Icosahedron
εικοσαεδρος 12 30 20