Four Kepler-Poinsot Polyhedra
Jump to navigation
Jump to search
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
![]() | This theorem requires a proof. In particular: needs considerable vision You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Historical Note
The fact that there can only exist Four Kepler-Poinsot Polyhedra 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)