Three Regular n-Dimensional Polytopes over 4 Dimensions

Theorem

Let $n \in \N$ be a natural number such that $n > 4$.

There exist exactly $3$ $n$-dimensional regular polytopes:

the $n$-simplex
the $n$-dimensional regular polytope corresponding to the cube
the $n$-dimensional regular polytope corresponding to the octohedron.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polytope
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polytope
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