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Results tagged with discrete-geometry
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user 20343
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
2
votes
Special case of Erdos Distance Problem in a plane
There has been recent progress on this problem published in the annals of mathematics:
On the Erdős distinct distances problem in the plane
Pages 155-190 from Volume 181 (2015), Issue 1 by Larry Guth …
- 1,441
8
votes
1
answer
442
views
Convex Polyhedra Scissors Congruence Problem
I am currently writing a geometry paper "Rectifications of Convex Polyhedra" and I am confused to have discovered what appears to be a remarkable discrete geometric fact:
Conjecture: Let $P$ be a con …
- 1,441
7
votes
1
answer
204
views
Are the primary parallelotopes classified? (equivalently, Voronoi cells of lattices)
A primary parallelohedron is a polyhedron that can fill space with infinite translated copies.
It is known (e.g., Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 29-30, 1973; or, Tu …
- 1,441
4
votes
1
answer
253
views
The Mahler conjecture and non-zonoidal 3-polytopes (4-polytopes)
I have been working on the Mahler conjecture for over a year now and have made some progress for certain classes of convex polytopes and I'm now attempting to write up my results specified to $\mathbb …
- 1,441