A cylinder has 0 vertices. If an edge is defined by the meeting of two faces then there are two edges but if an edge is defined by the meeting of two PLANE faces then there are 0 edges.
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A hexagonal cylinder has 8 faces, 12 vertices and 18 edges.
A cylinder has 3 faces, no vertices and 2 edges.
Three faces, two edges and 0 vertices.
Three faces, two edges and 0 vertices.
A cylinder has no vertices (not vertexes!) It has 2 circular edges.