# Mathematical Sculpture in Central Park

George W. Hart

What a cool thing to make in Central Park!  On Saturday, May 30, 2009,
we had a big sculpture-building party in the middle of New York City.

How do you make it?  You start by simply joining one piece to another.

Piece-by-piece a structure grows.

We are about sixty people, working picnic style on a beautiful afternoon.

With sixty helpers, the you can get a lot built.

These are Zometool parts that everyone is assembling into various modules.

I had first made one module of each type so everyone could copy them.

This particular module is quite versatile, with exciting sartorial possibilities.

Soon we have quite a few modules built and ready to put together.

Carefully, we join the modules into a single central structure.

There is a beautiful mathematical object underlying this, a 3D shadow of a uniform 4D polytope.

Deep concentration is required to get everything correct.

Many little details must be attended to.

Every part goes in a particular place in a particular direction.

Along the way, I explain some of the wonderful geometrical ideas.

Ta-da!  After three hours, the 10800 parts are assembled

Then we carefully carried it up a small hill to the edge of the main path.

Local New Yorkers and tourists from around the world had a chance to discover and appreciate it.

There is much to see.  It has ten hexagonal tunnels like this.

Later, we carried it off to be disassembled.  It had brief but inspiring life, like a sand drawing.

Thank you Jon Schweig, NY program director of Math for America,
for inviting me to lead an event. It was the first day for this year's new fellows.

Thank you to everyone who participated. Thank you also to Michael Lisnet for the excellent photography. For more information about the mathematics underlying this structure, see this paper:
• George W. Hart, "Barn Raisings of Four-Dimensional Polytope Projections," in Proceedings of International Society of Art, Math, and Architecture 2007, Texas A&M, May, 2007, available online in pdf form.