The Truncated 120-Cell
Among the Dinosaurs at the Tampa Museum of Science and Industry
Prof. George Hart

The image above shows a six-foot diameter model of the truncated 120-cell in the lobby of the Museum of Science and Industry in Tampa, Florida.  On November 1, 2007, we built this as part of the art exhibit associated with the conference Knotting Mathematics and Art, held at the University of South Florida (USF). This is a temporary exhibit celebrating of the beauty of mathematics, in the form of a large geometric sculpture.  Thank you everyone who participated.

On the table above, you can see all the material we needed---3680 Zometool parts.  I am standing amongst the students from the USF math club who started working with me around 1:00. Seated: Nicole Trapp, Helen Barclay, Dane Harmon and Jessica Couvertier. Standing: Enoc Santiago, Andrew Burrus, George Hart, Edy Urken, Nick Orletzky and Laura Torres.

We began by making stacks of tetrahedral modules (and eating cookies for strength).

Twenty almost-regular tetrahedra join together to make the blue truncated dodecahedron in the central core. Then more compressed tetrahedra are attached around it on all sides, and it looks like a giant virus.

More helpers arrived and the structure continued to grow outwards.

After working our way out to the exterior on one side, we put it down on the floor so we could come at it from all sides. We continually had to solve little puzzles about about which type of cell goes where.

It grew into a six-foot diameter sphere with many internal layers.

Here is the crew at 5:30 that evening, exhausted after four and a half hours of construction. In addition to the names above, we include Laura Handbury and Kaita Saito.

The next morning, before the museum opened, we moved it into the lobby.

Mathematically the form is a three-dimensional projection of a uniform four-dimensional polytope: The Truncated 120-Cell. Three truncated dodecahedra and one tetrahedron meet at each vertex. It is one of the fifteen uniform polytopes in the H4 family that can be made in projection with Zometool parts.