Six Regular 4-Dimensional Polytopes

Theorem

There exist exactly six $4$-dimensional regular polytopes:

the pentatope (also known as the $4$-simplex)
the tesseract
the $16$-cell
the $24$-cell
the $120$-cell
the $600$-cell


Proof


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$
  • 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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