</lurk>
In no particular order:
Tetrahedron, Cube, Icosahedron, Dodecahedron, Octahedron
There's probably a fancy name for the cube, but I don't know it.
I got beat to it, so the next one:
the sides have to be regular polygons, and the sum of the angles meeting at a corner has to be less than 360
for a triangle, this means 3, 4 or 5 per corner, giving us the tetrahedron, octahedron, and icosahedron
for a square this is 3, hence, cube
for a pentagon, this is also 3, hence dodecahedron
three hexagons make 2 Pi radians, hence they tesselate the plane
What's Euclid's Fifth Postulate?
<lurk>
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