A curriculum piece I'm working on, with project lead David Koski, is the enumeration of Zome buildable tetrahedrons and hexahedrons. Zonohedra are Zome's forte.
"Enumeration" has technical meanings, and in this context "dissection" is also apropos as in: given this polyhedron X made in Zome, what would its volume be in terms of phi-scaled S and/or E modules?
We lose some of our audience at this point, given S and/or E modules are not a middle school subject, their being building blocks in a little known set, featuring, in addition, A, B and T modules. Then come the Mite, Sytes, Kites and so on. Kit and Kat.
"Enumeration" has technical meanings, and in this context "dissection" is also apropos as in: given this polyhedron X made in Zome, what would its volume be in terms of phi-scaled S and/or E modules?
We lose some of our audience at this point, given S and/or E modules are not a middle school subject, their being building blocks in a little known set, featuring, in addition, A, B and T modules. Then come the Mite, Sytes, Kites and so on. Kit and Kat.
Symmetrical Tetrahedron: Syte: Two of the AAB allspace-filling, three- quanta module, asymmetric tetrahedra, the Mites__one positive and one negative__may be joined together to form the six-quanta-module, semisymmetrical, allspace-filling Sytes. The Mites can be assembled in three different ways to produce three morphologically different, allspace-filling, asymmetrical tetrahedra: the Kites, Lites, and Bites, but all of the same six-module volume. This is done in each by making congruent matching sets of their three, alternately matchable, right-triangle facets, one of which is dissimilar to the other two, while those other two are both positive-negative mirror images of one another. Each of the three pairings produces one six-quanta module consisting of two A (+), two A (-), one B (+), and one B (-).
Yikes!
None of this stuff is really hard though, just why would you want to learn it? Did they think it might help you in art school? I did. Design school too. What's cultural literacy without the Concentric Hierarchy as wrapped in Synergetics? American literature has its jewels too.
The database would let students retrieve zonohedra by label in some way. The Koski spreadsheet features a huge inventory of types. In other records, all 65 tetrahedrons are covered, ala Steve Baer.
I hate to be the bottleneck on this one. I don't have but a few samples of Zome and don't have the grant. I'd be bringing some database skills to the equation. We'd be using vZome. Build the shape, check its volume. Again, is working out with E & S modules worth anyone's time? I'm banking on the venture leading to new vistas.
