Tag Archives: Installation

We arrived on HMC campus around 9am on March 28th with supplies in tow. Peter had reserved a nice space outside the chemistry department to build and display our planned geometric structure.

I’ve used a lot of different materials to build Sierpiński Tetrahedra over the years, including mailing tubes and hula hoops, among other possibilities.

For this installation commissioned by the Dickinson College mathematics department, we chose a construction technique that goes all the way back to a construction from 2016, but this time with a twist. All previous installations done with this technique used only one length of rod, producing rigid equilateral polyhedra. But I had long wanted to construct a rhombic enneacontahedron, a shape that George Hart introduced me to with one of his artworks.

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 been a fair amount of discussion about the Pythagorean Theorem, we settled on the following construction that demonstrates an interesting and less-familiar related phenomenon in three dimensions.

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 Hexagons in Zig Zag, so the ideal targets consist of just pentagons and hexagons. With Euler’s formula for polyhedra and a little calculation you can determine that such a shape must have exactly twelve pentagons and almost any number of hexagons; the page for the event includes a table of candidates.

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.

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.

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. For these types of questions, what one really needs is to solve the (more computationally thorny) “inverse Life” question: what colonies of cells can give rise to a given configuration in the next generation?

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.

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.

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.