A couple speakers dropping out at the last minute left a hole in the Math & Art session’s schedule the other week at MAA MathFest 2024 in Indianapolis, IN. As the famous expression you’ve no doubt heard countless times goes: when life gives you cancellations, make cantellations!

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We arrived at Princeton early in the evening of August 5th with an assortment of the materials discussed in our planning post, ready to lead the PCMI/IAS Teacher Leadership Program in building an expanded icosidodecahedron.

Of the six possible box orientations, the participants chose to have the $6.125″$ sides form the edges of the triangular and pentagonal windows, the $4″$ sides form the edges of the rhombic windows, and the $2″$ sides provide the extra radial width:

The group was impressively self-organized, and after a brief presentation and selecting the box orientation, they were off to the races! They split into small groups to make modular braced pentagonal rings that could then be assembled into the final structure. Here is a time-lapse video of one group completing their ring:

In all the excitement, we forgot to take photos of the actual building! Using some low-res stills from our time-lapse, the key steps of this phase were:

Once twelve of these braced rings had been assembled, the group combined them by tying pipe cleaners together, leaving triangular and rhombic windows, and finally bracing the diagonals of the rhombi.

The teachers then designated a “coloring committee” to pick the decoration of the exterior faces of the boxes. They settled on making each “line of latitude” of the resulting ball of boxes uniform in color. With the scheme chosen, the units could be assembled to produce the final Amboxes installation:

While we were in the home stretch of building the above piece, the organizers Peg Cagle and Dena Vigil were just a little disappointed that it was only going to come out to about a meter in diameter. Since we had some time left in our 6pm-9pm slot, their colleague Brian Hopkins made a run to the store for more pipe cleaners and the group forked into a contingent that worked on finishing the above build and a contingent that started another, bigger build!

Since the radius of the sculpture is limited by the dimensions of our boxes, we improvised by attaching two boxes together end-to-end to create makeshift $2″ \times 4″ \times 12.25″$ boxes. The group elected to use this new, extra-long $12.25″$ side for the edges of the rhombi, using the $4″$ sides for the triangle and pentagon edges and again using the $2″$ sides as the radial “puff.”

The long diagonals of the rhombi were a good deal longer than the bracing material we’d prepared, since this ad-libbed structure was not one of our six anticipated builds. So we braced the short diagonals instead, using pairs of craft sticks joined to have the correct length.

Here is the finished second build:

Between the two constructions, there was plenty for everyone to do, and everyone really came together as a team to complete the project. Amboxes hung in the meeting room of the Teacher Leadership Program for the duration of the conference, and then its components were all recycled or taken by participants to use in similar activities in their classrooms.

We arrived on HMC campus around 9am on March 28th with supplies in tow. Peter had reserved a nice space outside the chemistry department to build and display our planned geometric structure.

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Over fifty members of the Occidental College community, organized by Prof. Jim Brown of the Math Dept., came together (Friday, 2023 Nov 10) to construct a Sierpinski-style fractal based on the regular octahedron. You can read more about it in the The Occidental weekly newspaper; more details will be posted here as time permits.

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