More Non-origami Modules
Another aspect of the PCMI session on Illustrating Math was a series of exploratory, hands-on workshops. One of them focused, in part, on the design of modules like the one for the truncated triakis tetrahedron, but based on other existing modular origami units.
It’s more or less possible to transpose any modular origami unit to a cut-and-score single-sheet module with tabs and slits, as the following table of designs from the workshop shows:
| Modular origami unit | SVG of cut-and-score design | DXF of design | Sample construction |
|---|---|---|---|
| Sonobe |  | Sonobe.dxf |  |
| Penultimate |  | Penultimate.dxf |  |
| 135° Unit |  | WS135.dxf |  |
| Reptile |  | Reptile.dxf |  |
A key difference that emerged from these workshop examples as compared to the PHiZZ units is that this plastic sheet material produced beautiful results on these geometrically exact units, whereas it did not distribute the slight geometric imprecisions inherent in PHiZZ unit constructions nearly as well as paper units do. (Many of the modular plastic PHiZZ constructions end up looking slightly lopsided, whereas the models from the workshop were all extremely crisp.) This distinction definitely plays into future material selection for geometric constructions.