There is one curved side and two curved edges (the rims along the top and bottom).
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There are no curved edges, but it does stack.
There are no curved edges on a triangular pyramid.
There are no curved edges in a pentagon. Part of the definition of any polygon is that they have straight edges.
Ah, what a delightful little shape we have here! It sounds like you're describing a cylinder, my friend. With its two flat faces, one curved face, and two curved edges, it's a lovely shape to paint happy little trees on. Just remember, there are no mistakes, only happy accidents.
The cylinder has 2 edges.