Mathcamp 2008

George W. Hart

Since 2000, I have visited Canada/USA Mathcamp for a week each summer as a guest lecturer. 
This page shows some of the activities I led in 2008.  Above is the world premiere of the truncated-ambo-120-cell. 
This is a projection of a uniform four-dimensional polytope with H4 symmetry, which we have built with Zometool. 

We started at 4:00, with roughly 100 campers making various truncated tetrahedron modules.

There are eight different shapes to build, spread among various student groups.

This was all happening as people were coming and going to meetings with their advisors.

With so many people we quickly built the core and some adjacent cells towards one outer facet.

Then we lifted it and turned it so that outer facet was on the floor and we could work all around it.

Once you learn the pattern, it is relatively quick to assemble.

It fills a sphere about 2 meters in diameter.

Working up to the top, we had about 8000 of the pieces in place after four hours of work, at 8:00.

For engineering support, we had vertical rods carrying some of the weight.

But then the bottom collapsed as we were adding more modules to the top.

Having learned a few things from the experience, we disassembled and started again.

About 20% of the original modules could be salvaged, and we worked faster with practice.

This time we worked more in the center at first. It clears the ceiling by 1/4 inch.

And we experimented with more and larger engineering supports for carrying the weight.

Things went very well, with a dedicated group of hard-core Zomers.

In this structure, at each vertex there are two truncated icosidodecahedra, a truncated tetrahedron, and a triangular prism.

A half hour after midnight, we were finished!  It is my new favorite polytope! Another name for it is the canti-truncated 120 cell.
It is the last of the fifteen H4 polytopes to be made.  I have now participated in the construction of all of them. 
There are 10800 parts (plus the scaffolding).  It is also the largest ever made in terms of volume.
You can read more about these polytope models here.

Another activity I did was a puzzle workshop, with various geometric puzzles. These paper pieces need to be assembled.

The H-puzzle is made from 30 cut paper parts.

This highly interwoven Meanders modular kirigami construction is pretty tricky.

It looks cool when finished in a perfect five-color pattern based on the compound of five tetrahedra..

Another activity was constructing this sculpture from 200 CDs.
It is based on a truncation of the rhombic triacontahedron.

I always do some Zometool workshops at MathCamp.  Here, we are making some polyhedral models.

And this is a 4D polytope workshop.  How often do you see four 120-cells in the same room?

In another workshop, we made a 2-layer geodesic sphere from TubeSpace parts. 
This is modeled after the Montreal Expo67 dome, with triangles on the outer layer
and a dual layer of hexagons inside. I wrote a Mathematica program to calculate
all the strut lengths. More information about the structure and construction is here.

I also took a break from math one day for a strenuous climb up Mt. St. Helens. 
This is a self-portrait at the rim of the volcano, looking way down into the crater. 
If you look carefully, you can see the steam venting out of the central lava dome.