You’d think I’d be searching for printers, not prints, however it’s the outputs I’m seeking, more than the process of making them. You might call me lazy for that reason, but as a Martian Math teacher on the front lines, in need of teaching supplies, I think I’m just doing my job in clamoring for A&B modules.
As you may see from the above pictures, the A module is none other than an orthoscheme of the regular tetrahedron (note: three right triangles). The B module (yellow, bottom figure) is what’s left over after an A has been subtracted from the regular octahedron’s orthoscheme.
Then comes the MITE (MInimum TEtrahedron) — a space-filler (cite Sommerville), with no need of “left” versus “right” versions — made of left and right A, plus either left or right B.
The MITE consists of face-bonded left and right orthoschemes, this time of the cube. We account it as 1/24th of a volume 3 cube in our “Sesame Street” canonical sculpture, and so with of volume of 1/8. A&B both have the same volume: 1/24.
A question for the 3D printing industry: would we want to print just the faces, as slabs, perhaps beveled, and then stick these together? The modules would be hollow and air-filled in that case. The plans have all been published.
The logical alternative is to 3D print them as solids, but wouldn’t that take too much material? Volume scales as a 3rd power of edge length, after all. Our regular tetrahedron might need an edge of at least three inches, but why stop there?
Once I have a stash of As and Bs, I can assemble them, which means they were designed with assembly in mind.
Filling them with liquid or a dry grain might be another option, as we’re involved with teaching about volume. I need to treat them like measuring cups, with which to calibrate other volumes. Think of cooking shows.
When we get to the S and E modules, scaling up and down by φ will be important.
Table 1: Scaling the E Module
e6 = (e3)(1/φ)(1/φ)(1/φ)
e3 = (E)(1/φ)(1/φ)(1/φ)
E = (√2)(1/8)(1/φ)(1/φ)(1/φ)
E3 = (√2)(1/8)
E6 = (E3)φφφ
Same with the S modules (…s6, s3, S, S3, S6…).
Such Tables gives us some of our Volume Identities.
I’m not suggesting we need this classroom supply instead of Python. My job is to help students merge their spatial thinking with their ability to compute more generally.
Martian Math has proved popular in the field, for just that purpose.