Boy's surface

You probably know the model of Boy's surface in front of the library of the research institute MFO in Oberwolfach (here you can find more information on Boy's surface). Some day I decided to rebuild a small model made out of paper strips. So I wrote a little Maple program which plotted the curved strips, printed and glued them to obtain the model seen on the left.

If you want to build one of your own, click here to download the plots.


You have to start with the star shaped plot. There are two types of stripes: The radial ones, marked with "r" and a number, and the concentric ones, marked with "c" and a number. The radial stripes have to be glued to the star. For example, the stripe r18 has to be glued to the ray with number 18 on the star (the starting point of a stripe is always the part with the number). Then the stripe r18´ has to be glued to the end of r18. Next comes r18´´ to the end of r18´. Opposite radial stripes are glued at their very ends to form Moebius strips, e.g. the radial stripes with numbers 3 and 18 are opposite. After this, you can glue the concentric stripes: Start with c1 and glue the yellow starting point to the first dot of r0, the second point on c1 to the first dot of r1, and so on. Continue with c2 and glue it to the second dots of the radial stripes, starting with r0. Some concentric stripes are divided into more than one piece (like the radial ones). The order is c3 then c3´1 then c3´2 for example.

You have to figure out which stripes pass over or under other stripes and this can be somewhat non-trivial. But puzzling this out may be a bit of fun. Send me a picture if you have built your own projective plane.

Here are some explanations behind the math of the model and here you can download the Maple files.