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"AI Overview" in Chrome says a polyhedron is:

"a three-dimensional geometric shape with flat polygonal faces, straight edges, and sharp corners or vertices"

which is not a bad definition in my view. Some of these polyhedra are familiar to us; for example here is a back-of-an-envelope sketch of some with 4, 5 and 6 faces.

Note that we are not concerned here with the particular angles or side lengths, just with the topology: how many faces and vertices there are, how many sides each face has, and what faces fit with what other faces around each vertex. 

The solid with 4 faces - a tetrahedron aka triangular pyramid - is the only possibility for 4 faces, and for 5 faces there are exactly two polyhedra - the pyramid with a quadrilateral base and the triangular prism.

The two hexahedra shown are not the only ones however. There are 7 altogether; can you find some or all of the remaining ones? Solution in the Comments.

As the number of faces grows the number of possible polyhedra climbs exponentially [1].

Numbers up 10 faces are exact, but those from 11 on are only estimated.

Amazingly Steven Dutch has enumerated and classified all 2606 enneahedra, finishing on 2 November 2016 [2].

Here's a quick question to finish - what is a regular hexahedron better known as?

References

[1] https://oeis.org/search?q=A000944&language=english&go=Search

[2] https://stevedutch.net/symmetry/polynum0.htm