Step-by-step instructions for making your very own Boy's surface
(A strange and beautiful embedding of a punctured projective plane).
First you will need a pattern.
Also, scissors (although a matte knife or single-edged razor blade is better)
and some tape.
Print the pattern three times. For best results, use as heavy
stock as is available for your printer.
Cut out the patterns.
Cut through the loop in one of your patterns and tape it back
together after linking it with another.
Now bring the "points" of the teardrop shaped cutouts together.
Curl-up one of the "legs" of one piece and position it so that
is is held by the teardrop-shaped hole in the other. Indeed, the
pieces can be positioned so that one leg of each piece is
curled up inside the hole of the other:
The last piece has to also have its loop cut, but it must be
reattached after linking with both other loops.
The last link has to be positioned in such a way that it will trap
both of the free legs of the previously assembled pair.
(Symmetrically, it's legs get curled up into the other pieces' holes.)
A few more bits of tape placed strategically will give
you a fairly sturdy Boy's surface.