A Modern-Day Sangaku

Prof. George Hart

An interdisciplinary activity and exhibit, that blends art,
mathematics,
computer science, and traditional Asian culture.

The image above shows me feeling good about completing this intricate geometric construction. On monday, April 24, 2006, I asked students, faculty, and staff to help me create a modern-day sangaku in Stony Brook University's Wang center. This is a celebration of the beauty of geometry, in the form of a large geometric sculpture.  Thank you everyone who participated.

We started at 10:00AM, working on a series of modules in five different shapes.

Each module is a projection of a truncated icosahedron, but there are subtle variations between them.

We began to accumulate the 75 needed modules.

We then started the core and strengthened the base.  (One participant just likes to chase balls...)

We worked up the central axis to the very top.

Then many people could construct from all sides attaching modules.

The sphere is 6.5 feet in diameter.

Standing on chairs, we could reach the top parts.

The outer layer of 30 flat modules went quite quickly.

We finished at 2:00, so the total time was four hours.

Here, the very last of the 10800 plastic components is attached.

I believe no one has ever made a physical model of this mathematical structure, so this is a world premier event.

It looks very cool when you step back and view it down a 5-fold axis of symmetry.

I like to feel that my work fits in with the Japanese tradition of sangaku. This is a display by devotees colorfully celebrating the beauty of geometry in a peaceful temple-like setting. For background information on traditional sangaku, see the event announcement page. It is scheduled to remain on display for two weeks, until the end of the semester. I will have a small disassembly event on friday May 5 when we take it apart and pack up the pieces.

Mathematically the form is a three-dimensional projection of a uniform four-dimensional polytope that doesn't have any reasonable name. One name (used in Norman Johnson's upcoming book on uniform polytopes) is The Cantitruncated 600-cell. I'd prefer to call it The Truncated Ambo 600-Cell (because that may help one to visualize it).  Whatever you call it, four polyhedra meet at every vertex: a truncated icosahedron, a pentagonal prism, and two truncated octahedra. It is one of fifteen uniform polytopes in a family with the same symmetry, and which can be made in projection with these Zometool parts.

Thank you Zometool for loaning me the parts for this event.

Photos by Kara Greenfield, Joseph Mitchell, and George Hart.