An ellipsoid with a slice removed.
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Sphere
Yes, the Platonic solids (excluding the sphere which does not have vertices).
According to Euler none; for all 3d shapes: Vertices + Faces = Edges + 2 ⇒ 12 + 8 = 19 + 2 ⇒ 20 = 21 So unless 20 does equal 21, no 3d shape has 8 faces, 19 edges and 12 vertices. Any 3d shape with 8 faces would be an octahedron.
edge
# of faces + # of edges + # of vertecies + 2