Möbius twists

 

A thin strip (of paper or springy metal or wood) can be bent into a ring by joining its two ends.  If you don’t twist the strip, you get a simple cylindrical ring, like a hoop that holds together the staves of a wooden barrel.  But if the strip is twisted before the ends are joined, the ring that is formed has what is called a Möbius twist, and it has some surprising properties.  A single twist (of 180°) will join the top edge of one end of the strip to the bottom edge of the other end, and produce a one-sided loop.  That is, you can trace a continuous path along the center line of the loop (parallel to the edges) until returning to the starting point, and in doing so, you will have traveled along the center line of both the front and back side of the original strip.

The polyline circuits and their curved counterparts that are skeletons for Bakker’s sculptures often twist as they visit points in the cubic lattice.   Möbius twists only become apparent when the skeletons are coated so their cross sections have rectangular shapes.  The cross-sections travel like a roller coaster car on the skeleton path, sweeping out the sculpture’s circuit.  The cross-sections of the coating are varied for aesthetic interest, but also must vary so that at the beginning and end of the circuit, the cross sections match and can fuse.   Only by tracing along an edge of the surface of a Bakker sculpture can you discover how many Möbius twists it makes.