Archimedean solid

A polyhedron whose faces are regular polygons and whose angles are all congruent. The faces may all be of the same type, in which case the solid is a regular polyhedron, or may be of different types. There are only thirteen Archimedean solids.
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Dual shapes form if the vertices are replaced by faces, and vice versa; the dual of a cube is an octahedron. b, A snub cube is an Archimedean solid — a polyhedron that has identical vertices but different types of edge and face.

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But Archimedes’ original list only had 13, and mathematicians have for the most part agreed with his list and use a definition of Archimedean solid that includes only those 13.

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It is a relative of the rhombicuboctahedron, which is an Archimedean solid that also has 24 vertices with three squares and one equilateral triangle around each vertex.

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The rhombicuboctahedron is an Archimedean solid, and ψρ is not.

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Just when you think you can give a short, simple explanation of what an Archimedean solid is, you have to launch into an description of a technical condition that is only necessary because of this one example!

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Archimedean Archimedes

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