7 Answers

Well one definition of a polyhedron is: “A 3dimensional solid with flat surfaces as faces. A polyhedron need not be convex or bounded.”
A cylinder fails this test because the sides are not flat, but rather are curved.

Is A Cylinder A Polyhedron

In classical mathematics, a polyhedron (from Greek πολυεδρον, from poly, stem of πολυς, “many,” + edron, form of εδρον, “base”, “seat”, or “face”) is a threedimensional shape that is made up of a finite number of polygonal faces which are parts of planes; the faces meet in pairs along edges which are straightline segments, and the edges meet in points called vertices. Cubes, prisms and pyramids are examples of polyhedra.
a cylinder is a quadric surface. There are no polygonal faces which are parts of planes

I think it might be V=2, E = 1 and F =1 . Imagine that you stretch the cilinder and you obtain a rectangular. ABCD where the vertex A is “identified” with B, the vertex C is “identified with” D, so the side AC is “identified” with BD. So there are 2 vertices, one edge AC and one face ABCD. Anyhow I don’t guarantee the proof( though such procedures are used in algebraic topology). But at wikipedia you finf the formula for Euler characteristic: The Euler characteristic of a closed orientable surface can be calculated from its genus g (the number of tori in a connected sum decomposition of the surface; intuitively, the number of “handles”) as χ = 2 − 2g. Now the cilinder is a orientable surface and its number of “handles” is 0, so X = 2 – 0 = 2 (not surprising) I need to read more algebraic toplogy.

a polyhedron is a solid formed by plane faces
a cylinder is a round (nonplanar) solid

It doesn’t consist entirely of flat surfaces, for a start.

it has rounded sides with no corners