Definition:Archimedean Polyhedron
Definition
An Archimedean polyhedron is a convex polyhedron with the following properties:
- $(1): \quad$ Each of its faces is a regular polygon
- $(2): \quad$ It is isogonal
- $(3): \quad$ The faces are not all congruent.
- $(4): \quad$ It is not a regular prism or a regular antiprism.
Also defined as
The pseudo-rhombicuboctahedron is also sometimes classified as an Archimedean polyhedron, but as it is not isogonal it is usually excluded.
Also known as
An Archimedean polyhedron is also known as a semi-regular (or semiregular) polyhedron, but $\mathsf{Pr} \infty \mathsf{fWiki}$ employs the use of the term semiregular polyhedron for a wider category of polyhedra.
Some sources use the term Archimedean solid.
Also see
- Results about Archimedean polyhedra can be found here.
Source of Name
This entry was named for Archimedes of Syracuse.
Historical Note
The Archimedean polyhedra were originally classified by Archimedes of Syracuse in a work, now lost, that was discussed by Pappus of Alexandria.
The first of the modern mathematicians to describe them was Johannes Kepler in his $1619$ work Harmonices Mundi.
Sources
- 1991: David Wells: Curious and Interesting Geometry ... (next): Archimedean polyhedra
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Archimedean solid
- Weisstein, Eric W. "Archimedean Solid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArchimedeanSolid.html