A shape in fewer than 3 dimensions.A shape with one or more curved faces or edges.
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Polyhedra (singular = polyhedron).
A polyhedron is a solid object bounded by polygons. Polygons are plane shapes [bounded by straight lines]. The curved surface of a cone is not a polygon and so the cone is not bounded by polygons and therefore, a cone is not a polyhedron.
A triangle is the only polygon with 3 corners (vertices). There is no polyhedron with 3 corners.
You can find a polyhedron with any number greater than 4 of vertices or faces. However, a torus, ellipsoid, sphere, paraboloid, hyperboloid are all standard shapes with no vertices. Cylinders, too, have no vertices. And there are many completely random shapes - a lump of putty, for example, which will have no vertex.
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