what begins life as a set of hyperbolic right hexagons...
...becomes a design for playground equipment. (it's like a hyperbolic
4-punctured sphere.)
held one way by Daina, it's a helicoid...
and held another way by David and Daina, it's a catenoid. It's
easy to see this transformation when looking at the crocheted model---but
really a pain to calculate it in differential geometry!