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]
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]
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]
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]
Here’s a picture of FireStar, a large-scale woven small stellated dodecahedron constructed by visitors to the open house of the Institute for Computational and Experimental Mathematics during Providence, RI’s WaterFire festival on 2019 Sep 28.
It’s high time that S∞ got back to its core: mathematical constructions you can build. Here’s an attractive star-shaped polyhedron made with a weaving technique that I am indebted to Jürgen Richter-Gebert for introducing me to. It’s called the “small stellated dodecahedron,” and is one of the
A few days after the event at TCNJ, students at the PROMYS program at Boston University built another “Life sculpture” in which each layer is a generation and time proceeds downwards. Here, we explored questions of how you might know things like whether the resulting “sculpture” would be connected, or whether it would be self-supporting.… [Read more]
Here is a photo of the first 13 generations of the evolution of the “R” pentomino pattern in John Conway’s Game of Life. Each layer represents one generation, and time proceeds downwards. In each layer, live cells are represented by boxes. The color of the box indicates how many generations that cell has been alive:… [Read more]
Here’s an image from inside one of a pair of mirror-image snub dodecahedra built by passersby on the Harvard Science center plaza in 2019 April. The completed work, “Spectral Snub”, was on display inside the Science Center for the following four days. Photo courtesy of Stepan Paul.
Here’s a torus built from equilateral-triangle Geometiles that I used as a prop for an undergraduate talk at Harvard University in the Fall semester of 2018. Actually, the structure it is based on is not mathematically exact; the triangles theoretically are isosceles triangles of sides 1, 1, and 0.998, but there is plenty of give… [Read more]
This is a placeholder post for pictures of an installation I led on 2018 Oct 21 at the Mathematical Sciences Research Institute, entitled “Tetrahelix”. It consisted of a double helix, one strand of which was composed entirely of regular tetrahedra connected face-to-face (such compounds can reach any point in space and come arbitrarily close to… [Read more]
Here’s a a student-built snub dodecahedron that resulted from a session I led in July 2018 at The College of New Jersey. It uses the classic “marshmallow and toothpick” construction technique, just with styrofoam balls in place of the marshmallows and 1/8″ diameter dowels in place of the toothpicks. For geometric accuracy, the students did… [Read more]