Ambagesque

# George W. Hart

Ambagesque (from the Latin word for "tangle") is a five-foot diameter wooden sculpture at Macalester College in St. Paul, Minnesota.  Commissioned by the Department of Mathematics, Statistics, and Computer Science, it was assembled by students at a "sculpture barn raising" and installed March 22, 2016.

You can get a better sense of the structure from this video of it rotating.

I like that it is installed so that it can be seen from either above or below.  That allows viewers to get a better sense of its geometry.

Because it could initially appear like a confusing tangle, it might require some study to realize that it consists of sixty copies of a single flat shape, shown in the template above.  The shape is carefully designed to exactly meet with itself in many ways.

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At the assembly event, I led students in the process of connecting the pieces with cable ties.  The parts are made of 1/4-inch thick plywood. The first step is to join two components into a simple module.  But it is not really so simple, as there is already an issue of handedness that must be considered.

The modules are then connected together in specific ways to make a variety of openings.

Each part connects to other parts in six places, so it is highly interconnected and rigid.

As it grows, the structure begins to take form and the symmetry becomes apparent.

The structure has icosahedral symmetry, with 2-fold, 3-fold and 5-fold rotational axes.

Looking straight into a 5-fold axis gives a good view.  There are twelve such openings around the sculpture.

When the plastic cable ties are all in place, we pause to take a group photo, but it is not finished yet.

We replaced the plastic cable ties with metal cable ties, which are permanent, and the buildings people suspended it.

It is hanging in the two-story atrium of the Olin-Rice building if you would like to visit it.

To get a better sense of the assembly event, see this video by August Halverson.

Thank you to everyone at Macalester who participated, especially
Tom Halverson, who organized the many excellent arrangements.
There are many more photos in the article Making Math Beautiful, by Alexandra McLaughlin.

I later made a small version of this design from fluourescent acrylic, shown here.