Thirteen Archimedean Polyhedra

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): $13$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polyhedron: 1. (plural polyhedra)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polyhedron: 1. (plural polyhedra)
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Archimedean solid
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Archimedean solid
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