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Results tagged with discrete-geometry
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user 30800
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
8
votes
Tiling a rectangle with a hint of magic
There is an unpublished note on this theorem from 1987 by Edgser W. Dijkstra, On a Problem transmitted by Doug McIlroy, see also this summary. He explains how the proof that uses complex double integr …
- 1,083
3
votes
Accepted
How are reflection groups related to general point groups?
Here is a more worked-out and concrete version of the proposed counterexample mentioned in the "Update" of the post.
We start from a symmetric arrangement of 12 great circles $F_1,\ldots,F_{12}$ on …
- 1,083
1
vote
Accepted
Expected minimum face angle of random convex polyhedron in $\mathbb{R}^3$
The answer is YES. (I am assuming you mean the angle between two adjacent edges on a common face. (The dihedral angles all go to $\pi$.)) The easy and brief reason is that, in a large random point set …
- 1,083