Infinity symbol in bookbinding to indicate that a book is printed on acid-free paper and will therefore be long-lasting. In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its own tail that has also come to symbolize the infinite, and the ouroboros is sometimes drawn in figure-eight form to reflect this identification, rather than in its more traditional circular form. In the works of Vladimir Nabokov, including "The Gift" and "Pale Fire", the figure-eight shape is used symbolically to refer to the Möbius strip and the infinite, for instance
Duocylinder flat tops. This operation is equivalent to removing select vertices/pyramids from polytopes, but since the 3-sphere is smooth/regular you have to generalize the operation. The dihedral angle between the two 3-d hypersurfaces on either side of the ridge is 90 degrees. Parallel projections of the duocylinder into 3-dimensional space and its cross-sections with 3-dimensional space both form . Perspective projections of the duocylinder form torus-like shapes with the 'doughnut hole' filled in. The duocylinder is the limiting shape of duoprisms as the number of sides in the constituent polygonal prisms approach infinity. The duoprisms therefore serve as good polytopic approximations