# CategoryPolyhedra

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A polyhedron (plural: polyhedra) is a many-faced 3-dimensional shape. A regular polyhedron has identical faces all with sides of the same length, and vertices of the same angle.
That definition leaves something to be desired - I think it would make any double-pyramid regular.
It would indeed. I think we want...
I don't think it would.  Mind you, I'm currently trying to work out why two tetrahedra, base to base, aren't regular.  My poor brain.
Because there are 4 triangles around each of the glued vertices, and only 3 around the two unglued vertices. I'm not sure your example actually fits "vertices of the same angle".

A regular polyhedron has identical regular-polygonal faces, meeting in identical configurations around each point.

There are FiveRegularPolyhedra, known as the PlatonicSolids.

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