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...n|polychora]], plus ten stellated ones. Above four dimensions, only three regular polytopes exist in each dimension, all of which are convex, and each of whi ...erfect rotational symmetry in any direction, for instance, but a [[regular tetrahedron]] only has rotational symmetry through axes passing through the centers of

...e]] that emits beams of [[light]] from four points arranged in a [[regular tetrahedron|tetrahedral]] pattern. Two levers next to the sphere set it in [[rotation]

The area of a [[regular polygon]] of ''n'' sides each of length ''s'' is <math>\frac{1}{4} n s^2 \c ...e area&mdash;indeed, exactly the same as the surface area of the [[regular tetrahedron]] it starts with, since each iteration adds surfaces of the same total area