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Results tagged with discrete-geometry
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user 39120
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
2
votes
How many small dots can be drawn in a region such that no three are "collinear"?
Well one observation is that if three dots are not "collinear" then the triangle formed by all of the centers has the lengths of its altitudes being at least $r$. This implies that the area is at leas …
- 2,242
25
votes
Accepted
Can a convex polytope with $f$ facets have more than $f$ facets when projected into $\mathbb...
Consider the polytope in $\mathbb{R}^3$ with $8$ vertices at coordinates $(\pm 1, \pm 2, 1), (\pm 2, \pm 1, -1)$. Geometrically this looks like a cube where the top face is stretched in the direction …
- 2,242