From new.math.uiuc.edu/oldnew/calculart/ These figures are all 3-D shadows of surfaces embedded in spherical (positively curved) space. The Snail begins as a Moebius band whose boundary is a planar circle. Next, the circle is drawn together to form a closed crosscap surface. Fly inside to see the pinchpoints and their Whitney umbrella neighborhoods. Rotating this projetive plane in 4 space morphs its 3 shadow from the crosscap to Steiner's Roman surface. Next we give the ribbon a second half twist, which expands to form a Clifford torus. Note the Hopf circles, every pair link each other once. It's fun to fly inside. It finishes with Brehm's Knotbox. To the topologist, the Knotbox is a standard spine for the complement of the trefoil knot in the 3-sphere. Think of a bicycle inner tube, but tied in a knot; blow it up until there is no place left in the universe to expand it into. The rubber walls will merge into a 2-dimensional shape. It could be the Knotbox.