The two-dimensional manifolds are non-Euclidean in that the perimeter of a small circle of given radius on the surface is greater than that of one of the same radius on the plane (which in turn is greater than one of the same radius on the surface of a sphere). A beetle exploring the surface would find its world to be complex in its labyrinthine interconnections.
Beyond the representation of the human figure, 3-D sculpture is
disappointing. Cezanne said: "Treat nature in terms of the cylinder,
the sphere, the cone, all in perspective". Barbara Hepworth was renowned
for being the first sculptor to make a hole through a piece of stone
in an abstract design, but artists now have many more interesting
geometrical objects than the torus.