I would personally choose Platonic Solids, every time.
In her book Geometry, Michèle Audin says,
In this section, I want to prove that there are five types of regular polyhedra in 3-dimensional space.
with the footnote
In my opinion, this statement is part of the cultural heritage of mankind, as are the Odyssey, the sonatas of Beethoven or the statues of Easter Island (without mentioning the Pyramids) and I cannot imagine how a citizen, a fortiori a maths teacher, could not know it.
I think she has a wonderful (if somewhat scathing!) viewpoint on this particular facet of geometry, and sadly, I don't know how often students meet polyhedra.
In 45 minutes, you should have time to
Introduce the Platonic Solids, although you really should have paper or wire-frame (e.g. Zometools) models for this.
Prove that at most five Platonic Solids exist (by examining how much of $360^\circ$ is taken up by various numbers of regular polygons, around any vertex). It's very elementary, although requires some explanation.
with time to spare. Good additional topics are to
Count faces of each dimension (probably not combinatorially, just by inspection. I've had students who have a hard time with the icosahedron, due to all the symmetry!) and verify Euler's famed $V - E + F = 2$ formula (which of course holds more generally than just for Platonic Solids).
Verify Descartes' Total Angular Defect Theorem (add up all the angles in a given vertex; that's the angular defect of that vertex. The sum of these defects, over each vertex of the polyhedron, is $720^\circ$), which also holds more generally than for just Platonic Solids.
I like these last topics because they show us that the world has some very cute, but not at all obvious, rules about what is physically possible; restrictions by the very nature of three-dimensional space!