Archive for the ‘polyhedra’ Category

Metal Trees


Roxy Paine’s sculpture “Defunct” (photo, Nicole Marti) There were a couple of seminars today and one mentioned a result giving the following interesting corollary. Suppose we have a graph , and with each edge e we associate three numbers which we interpret in the following way: to construct edge e we need to use kilograms […]

This week I have been at EPFL, Lausanne, Switzerland. It has been a good opportunity to practice my French; there is not as much English spoken here as in the more touristic parts of the country. Nonetheless this is a good place to come if you are a tourist: it is nearby the beautiful lake […]

Exhibit A: Maple, a sapling of the University of Waterloo. It is a computer algebra system allowing you to perform both symbolic and numerical computation. It has lots of built-in “packages” including one called GraphTheory, and other people can design add-on packages as well, such as convex (for polyhedral combinatorics, related to linear programming). Exhibit […]

After figuring out why the equation in the last post described a tetrahedron, I was able to apply the same technique to generate the four other Platonic solids. By popular demand, here they are! The rounded cube has equation (1-x2)(1-y2)+(1-y2)(1-z2)+(1-z2)(1-x2)=0 and the rounded octahedron is 1-2(x2+y2+z2)-2(x2y2+z2x2+y2z2)+x4+y4+z4=0. I won’t post the icosahedron and dodecahedron’s formulas because […]

Bill Cook gave a talk at Waterloo about some of his work on the Traveling Salesman Problem (TSP). He has worked in the area for something like two decades. Here are some notes and highlights of his talk. One of his main research interests is the solution of TSPs to optimality. It’s worth pointing out […]