i think it is a cylinder
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I do not think such a figure can exist unless its "face" is a fractal of some sort.
A sphere has no edges or edges but its face is globular.
cylinder
sphere
a sphere has 0 vercites and 0 edges and 1 face its like a ball which has 1 face so it is round like the earth and has no edges like a square and has no vercities like a rectangular triangle or a squared based pyramid