Weave a catenoid, get a helicoid free!

1. Print two copies each of the pictures below. Standard (80 gsm) A4 paper will give a reasonable balance of stability and flexibility, and yields a catenoid about 10cm tall and wide. (More refined version.) For a larger model you can use A3 paper, but may want to use thicker 160 gsm paper for more stability.

   

2. Cut out all the annular strips (ie two of each size) and 25 of the "ribs", and two halves of the "thick" rib.

   

3. Glue all the annular strips to one of the half-ribs (with the straight edge of the half-rib outward), alternately above and below. (It is easiest to first glue all the ones that go underneath, and then all the ones that go on top.) The result will look something like this.

   

   For added stability, secure with some tape over the edge of the half-rib.

4. Weave in the other ribs, gluing them to the outermost annular strip (only). The first two are very fiddly, but then the catenoid begins to take shape and it gets easier.

   

5. Weave in the final half-rib, glue it to all the annular strips, and tape over. This is also rather fiddly.