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Results tagged with discrete-geometry
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user 3568
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
3
votes
Accepted
Number of Hyper-cube cuts
Here is some handwaving which suggests that the growth rate is faster than polynomial.
For any cut of a d-cube, we can pair that with 2^d cuts of a parallel d-cube to get at least 2^d many cuts of a …
- 1,036
1
vote
Empty lattice simplex or White's theorem
I have not looked at the literature, so the following may fail for some geometric reason of which I am unaware; this reflects my thinking, and I do not yet see how else to get the results.
It should …
- 1,036
0
votes
Vertex-transitive polytopes in any dimension with any number of vertices?
For v prime, I don't know. For v even, and d=3, one can take a regular polygonal prism. I can think of toriodal versions for odd composite v, but I am unsure they are vertex transitive. I can go to …
- 1,036
7
votes
Covering a unit ball with balls half the radius
Here is an idea which should generalize to dimensions 2 and greater. I will start with dimension 2.
Let us place a circle of radius 1/2 in the center of the radius 1 ball. We will place most, if n …
- 1,036
1
vote
Tessellating $\mathbb{R}^n$ by bricks.
I will go out on a limb and pretend I understand the question and suggest the following for an answer.
Mark's example of 1x2 bricks in two dimensions can be modified to use 1x1 bricks, perhaps at th …
- 1,036