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4 added 13 characters in body

Following up on Joseph's comment: Branko Grünbaum and other others have pointed out that besides the 13 or 14, there are also two infinite families of polyhedra meeting the definition of Archimedean, although generally not considered to be Archimedean. Why prisms and antiprisms are excluded from the list has never been clear to me.

In any case, this is not just a historical curiosity --- in any attempt you make to classify them, you should run into these two infinite families.

If you use a modern definition, i.e. vertex-transitive, then you will also get 13 others. And a little group theory can help in the classification. If you use a more classical definition, i.e. "locally vertex-regular," you will indeed find a 14th.

3 added 53 characters in body

Following up on Joseph's comment: Grünbaum and other have pointed out that besides the 13 or 14, there are two infinite families of polyhedra meeting the definition of Archimedean, although generally not considered to be Archimedean. Why prisms and antiprisms are excluded from the list has never been clear to me.

In any case, this is not just a historical curiosity --- in any attempt you make to classify them, you should run into these two infinite families.

If you use a modern definition, i.e. vertex-transitive, then you will also get 13 others. And a little group theory can help in the classification. If you use a more classical definition, i.e. "locally vertex-regular," you will indeed find a 14th.

2 deleted 35 characters in body

Following up on Joseph's comment: Grünbaum and other have pointed out that besides the 13 or 14, there are two infinite families of polyhedra meeting the definition of Archimedean. Why prisms and antiprisms are excluded from the list has never been clear to me.

In any case, this is not just a historical curiosity --- in any attempt you make to classify them, you should run into these two infinite families.

If you use a modern definition, i.e. vertex transitivevertex-transitive, then you will also get 13 others. And a little group theory can help in the classification. If you use a more classical definition, and only require that the solid i.e. "looks the samelocally vertex-regular," at every vertex, you will indeed find a 14th.

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