Four Kepler-Poinsot Polyhedra

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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



Historical Note

The fact that there can only exist Four Kepler-Poinsot Polyhedra was demonstrated by Augustin Louis Cauchy in $1812$.


Sources