Amboxes: Planning
With the PCMI/IAS Teacher Leadership Program build approaching, it’s time to pin down some details. We’ve used boxes to make a “cuboxtahedron” and wanted to work with a different symmetry, so we’ve selected the expanded icosidodecahedron as discussed at the end of this MathStream post:
The hosts pretty much gave Studio Infinity free choice of what to construct, but requested that the materials be recyclable or reusable. In other words, it was important to the organizers to minimize the negative environmental impacts of the activity. For this reason, we’ve decided to reuse some rectangular craft kit boxes donated to Studio Infinity by Primed Minds. Since the boxes are $2″ \times 4″ \times 6.125″$, there are six different ways they could be oriented to constitute the rectangular faces:
The boxes are rigid, so the rectangular faces will be rigid, as will the triangular windows. On the other hand, the open parallelograms and pentagons leave the overall structure nonrigid without some bracing.
For the pentagons, support struts will be woven into pentagrams (or when they’re too short to weave, simply placed along two diagonals for a triangulation). For the parallelograms, we will add support struts along the long diagonals. (Small discrepancies in the lengths of the long diagonals should affect the geometry of the final model less than similar discrepancies in the short diagonals.)
Again, we want inexpensive, easy-to-use, recylable or compostable materials. Therefore, we will use off-the-shelf wooden/bamboo coffee stirrers, craft sticks, and/or chopsticks that come in the necessary lengths to match with the craft boxes, depending on the orientation that the participants choose for the boxes. The boxes will be connected with pipe cleaners threaded as discovered by a participant in an earlier build. It’s true that pipe cleaners are not recyclable, but they will be easily recoverable from the construction when it is disassembled and can be reused.
Based on the proportions previously discussed, we found the following items for the struts we might need:
| Pentagon side length | Bracing material (per pentagon) | Total count |
|---|---|---|
| 2″ | (2) half 6.5″ coffee stirrers | 24 |
| 4″ | (5) full 6.5″ coffee stirrers | 60 |
| 6.125″ | (5) 10″ craft sticks, hand drill | 60 |
| Rhombus side length | Bracing material (per rhombus) | Total count |
|---|---|---|
| 2″ | (1) half 7″ coffee stirrer | 30 |
| 4″ | (1) full 7″ coffee stirrer | 30 |
| 6.125″ | (1) 10.5″ chopstick | 30 |
Note that we don’t plan to use all of this. The participants will have their choice of which of the six different box orientations they want to use, so we want to show up prepared to build any of them. In addition, we’ll need 60 boxes per model and plenty of pipe cleaners (and some gaffer’s tape as always in public builds, to patch anything up that’s not quite as secure as planned).