Thirteen Archimedean Polyhedra
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Theorem
There exist exactly $13$ distinct Archimedean polyhedra:
- Truncated tetrahedron
- Cuboctahedron
- Truncated Cube
- Truncated octahedron
- Rhombicuboctahedron
- Truncated cuboctahedron
- Snub cube
- Icosidodecahedron
- Truncated dodecahedron
- Truncated icosahedron
- Rhombicosidodecahedron
- Truncated icosidodecahedron
- Snub dodecahedron
Proof
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
- 1991: David Wells: Curious and Interesting Geometry ... (previous): Archimedean polyhedra
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Archimedean solid