# Whimsy

### George Hart

Whimsy is a 30-inch diameter wooden sculpture with a confusing geometric structure.  Each piece is flat and connects two neighboring vertices, and each vertex is locally convex, but the overall sculpture is not convex.  It takes a bit of thinking to understand how that can happen.  The photo shows me next to it along with Reza Sarhangi (Bridges Organization president), Michael Pearson (MAA Director), and Bob Devaney (MAA president).

The sculpture was assembled at a "mathematical sculpture barn raising" I led at the Joint Math Meetings in Baltimore, MD, January 17, 2014.  A great many people helped over a three-hour period.  Here you can see one of the initial steps, in which five parts are glued and clamped to a jig by a group of five volunteers.

I made special jigs to hold the components in the proper relative position while the glue dries.  Everything needs to be very exactly aligned in order for the parts to meet precisely.  Specially modified clothes pins serve as clamps.  Each new group of five participants watched the previous five to see how it works.

I prepared the parts ahead of time in my studio in New York and brought everything with me to Baltimore.  The parts are made of 1/4" thick five-ply Baltic birch plywood that I laser-cut to the proper shape.  I beveled the mating surfaces with a sander to create the proper dihedral angles.  And I cut small slots in the mating faces for tiny custom "biscuits" that fit inside the ends of the parts.  The biscuits are laser-cut from 1/16" thick aircraft plywood to keep everything aligned.  They add a great deal of strength to the structure.

I wasn't sure how a bunch of mathematicians would do when asked to glue biscuit joints --- sometimes mathematicians get a reputation for abstractness rather than practical ability --- but it worked out great!  This is the first time I tried out the technique at a sculpture barn raising and everyone understood it easily.  So I'll certainly use it again in future sculpture activities.

After the glue sets on the five-part modules, we take them off the jigs and they are assembled three-to-a-vertex like a regular dodecahedron.  Plastic twist ties suffice to hold them together while the glue dries.  Many people can work simultaneously from all sides, so everything comes together pretty rapidly.

If a bit too much glue is applied and some oozes out, I can clean off the extra with a razor blade.  (I pre-finished the parts with tung oil, which helps repel glue from the surface.)  But not much cleanup was needed.

The final sculpture came out beautifully.  The joints are all neat and crisp, the way I like them.  Whimsy is now on display at the headquarters of the Mathematical Association of America (MAA) in Washington DC.

Before making the 30-inch version at the JMM conference, I made a smaller 10-inch version from cherry, partly as practice and partly to make sure I really like the design.  It can be seen on this page.

To learn about the mathematical structure underlying Whimsy, see this video.

Thank you to everyone who participated.
Thank you to Ginda Fischer and the MAA for some of the above photographs.
And thank you to SIGMA-ARTS/MAA and the Bridges Organization for sponsoring this project.