# 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 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.