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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

2 votes

Drawing 3-configurations of points and lines with straight lines

Let's try this again. If there weren't a degree constraint on the graph, then you could adapt the proof of Mnev's universality theorem (see my previous answer) to show that the problem was equivalent …
Peter Shor's user avatar
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5 votes

Forbidden mirror sequences

Here is a possible way of producing such forbidden configurations. Suppose you have $(ab)^k$ for some large $k$. Then I'd like to claim that $a$ and $b$ must be nearly parallel (see Thurston's answer) …
Peter Shor's user avatar
  • 6,342
5 votes

Drawing 3-configurations of points and lines with straight lines

Ten minutes ago I gave the wrong answer. I said: "You haven't mentioned Mnev's universality theorem, so I'll assume you don't know about it. Bokowski and Sturmfels is too old to refer to it, and for s …
Peter Shor's user avatar
  • 6,342
8 votes

How to generate a net on a 8-dimensional sphere

If you're looking for points on the 8-dimensional sphere, another thing you could do is go to Neil Sloane's table of spherical codes, scroll down until you get to dimension 8, and obtain a sphere cove …
Peter Shor's user avatar
  • 6,342