23 Apr

Pythagoras Cubed

I was recently invited at the last minute to lead a mathematical construction for a seminar for math majors at Loyola Marymount University. The hope was to create something physical connected with one of the topics in the course, which linked the history of mathematics with various unsolved problems, among other things. Since there had… [Read more]

09 Apr

Tessellating Truncated Octahedra

With all of the recent activity at Studio Infinity on geometric units that can be automatically cut and scored, it was natural for the S∞ G4G14 giveaway to be the 14-sided Truncated Octahedron, which tessellates to fill space. The additional challenge here as compared to some of the earlier interlocking structures was to ensure that… [Read more]

09 Apr

Assembling a TTO

These are the assembly instructions for the Tessellating Truncated Octahedra; you’ll find background and the cut files for them on them in the following post. Materials Two TTO pieces per unit you wish to build The first order of business is to fully cut and punch out two of the pieces from the cut templates… [Read more]

09 Apr

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… [Read more]

09 Apr

Truncated Triakis Tetrahedron

Materials 42 modular units cut out and folded (see Modular Origami, without the origami)(preferably 9 each of four colors and 6 of another) For the actual building event mentioned in the previous post (linked above), participants could choose from a variety of target polyhedra. The origami inspiration was the PHiZZ unit, which stands for Pentgons… [Read more]

08 Apr

Modular Origami, without the origami

In many ways, modular origami is ideally suited for the type of exploratory mathematical play that S∞ is dedicated to: it’s easy to get started, very tactile, and offers nearly endless opportunities for creating interesting and beautiful objects. For example, here’s a PHiZZ unit torus that resulted from a workshop I led at The Brearley… [Read more]

23 Mar

Woven GSD

Materials Tools 30 equal-length rods Measuring Tape 32 rubber bands Scissors This is a sequel to a (pre-pandemic) post about weaving a stellated polyhedron. This time, I’d like to show how similar techniques can also be used to create a “great stellated dodecahedron” (“GSD” for short; illustration to the left). The materials are in fact… [Read more]

19 Mar

Wiredodeca

After seeing Laura Taalman’s inspiring 3d print, it occurred to me that one could also render the edge-to-edge cubical array of dodecahedra contemplated in this earlier post in an analogous way. Plus, I just received a new Prusa SL1 printer, and needed something to try it out on. So after just a bit more tinkering… [Read more]

12 Mar

Wirecosahedra

When I showed this recent post to my friend and colleague Laura Taalman, aka mathgrrl, she suggested that another approach to creating a model of the underlying structure would be to construct the icosahedra themselves (rather than the negative space), except use wireframes of the icosahedra rather than solid ones to avoid obscuring all of… [Read more]

09 Mar

Anticos

Judging from at least one of the previous projects, Studio Infinity is intrigued with connecting polyhedra edge-to-edge. (Of course, connecting them face-to-face is interesting, too, but that’s pretty familiar from Legos and such; and vertex-to-vertex is the same as connecting dual polyhedra face-to-face.) As you can see in the “blueprint” for the Boxtahedral Tower at… [Read more]

08 Mar

Antidodec?

This MathStream post about why an icosahedron inscribes in a cube also shows that a dodecahedron fits into a cube in an analogous way. That raised the prospect that it might also be worth building an “Antidodec” analogous to the Anticos. So I quickly mocked one up in OpenSCAD (here’s the two files you need),… [Read more]

07 Dec

Math’s Bubbling (not) Over

Here’s a large-scale model I designed of the Weaire-Phelan space packing, built by the participants of the Fall 2019 semester on Illustrating Mathematics at ICERM in Providence. The title above is a reference to the fact that it is still not established whether this is the most surface-area parsimonious way to divide space into cells… [Read more]