Four Kepler-Poinsot Polyhedra

Theorem

There exist exactly four Kepler-Poinsot polyhedra:

$(1): \quad$ the small stellated dodecahedron
$(2): \quad$ the great stellated dodecahedron
$(3): \quad$ the great dodecahedron
$(4): \quad$ the great icosahedron.


Proof


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Historical Note

The fact that there can only exist was demonstrated by Augustin Louis Cauchy in $1812$.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9$
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Poinsot, Louis (1777-1859)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polyhedron: 1. (plural polyhedra)
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