SOLID MODELING 253
real projective plane or a cross cap which, again, cannot be constructed in three-dimensions without
self intersection. Another way to model a projective plane is to connect each point on the rim of a
hemisphere to a corresponding point on the opposite side with a twist. The third way is to attach a disc
to a Möbius strip making it a closed surface without boundaries.
(a) Instructions for building a torus
(b) Instructions for building a Möbius strip
(c) Instructions for building a Klein bottle, the usual projection and that
generated by revolving a figure ‘8’
(d) Instructions for building a Real Projective plane or a cross-cap (rightmost figure) from a
rectangular paper
Figure 8.9 Some basic surfaces.