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It is a well known geometrical fact that if you wish to construct solid, three-dimensional bodies whose sides are regular polygons (polygons whose sides are all the same length), try as you might, you will end up with no more than five such bodies. This result is a geometrical theorem --in 3D space there exist five and only five regular, or “Pythagorean,” solids. It has nothing to do with the state of our mathematical knowledge or our technological prowess. Like the statement that parallel lines meet at infinity, the existence of no more than five regular solids is an inescapable property of three-dimensional flat space.
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