Intrigued by regular polyhedra for years

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I've been intrigued by regular polyhedra for years, and have oft tinkered with them.

Can someone provide the "textbook definition" of a regular polyhedron?
 
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A "regular polyhedron" is a polyhedron, all of whose faces are regular polygons AND all of whose polyhedral angles are congruent.

If you add the requirement that they be convex (and was classically the case) then only the 5 "Platonic solids" are regular polyhedra. If you allow concave polyhedra, then there are 4 additional regular polyhedra.
 
Fantastic. I was specifically looking to find out whether convexity was a requirement.


Can you point me at some links that explore the additional 4 polyhedra?

Also, the "polyhedral angles" - are they merely the angle joining two adjacent polygons?
 

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