Construct a cylinder with a slit along a spiral. 
Wrap the graph of y = sin 2x around a cylinder. 

Place the smooth surface on top on the above surface. 
Construct the Monkey's Saddle: 
Carve out the Monkey's Saddle out of a solid cylinder: 
Construct onehalf of a solid cylinder as thus: 
Construct the region enclosed by the two
cylinders with equation
x^{2} + z^{2} = 1 y^{2} + z^{2} = 1 
Construct onehalf of the above surface as thus 
Construct this surface: 
Construct this onehalf of a solid torus: 