Definition:Archimedean Polyhedron

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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 vertex-transitive
$(3): \quad$ 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 considered along with these, but as it is not vertex-transitive it is usually excluded.


Also known as

An Archimedean polyhedron is also known as an Archimedean solid.


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