Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with discrete-geometry
Search options not deleted
user 22608
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
6
votes
Accepted
Regularity of Delaunay triangulation of a hypercube
"Finally my question is: how to triangulate a hypercube resembling (B)?"
This is easy to do, and is normally called the "standard triangulation" of the $n$-cube. Consider all the monotone edge paths …
- 1,502
13
votes
Accepted
Does the Hirsch conjecture hold for $n < 2d$?
The answer is no, as follows from the following Lemma of Klee and Walkup:
Lemma: If P is a d-polytope with n facets and we perform a "wedge" over any facet F we get a (d+1)-polytope P' with n+1 facet …
- 1,502
3
votes
Average vertex degree in finite Delaunay triangulations in high dimensions
Let me point out a very significant difference between dimensions 2 and 3. In dimension 2 ANY triangulation (Delaunay or not, random or not) has average degree strictly smaller than six (and going to …
- 1,502
3
votes
Vertex-transitive polytopes in any dimension with any number of vertices?
Gale transforms allow to settle the case of odd $d$ and even $v$ completely, in the positive (Matteo's answer in this case needed $v\ge 2d$).
Remember that the Gale transform of a $d$-polytope with $v …
- 1,502
7
votes
Accepted
Integer decomposition of dilated integral polytopes
The answer is YES in the following stronger form:
Lemma 1: Let $d>n$ and let $p\in dP\cap \mathbb{Z}^n$. Then there is an $i\in\{1,\dots, n\}$ and points $p'\in iP\cap \mathbb{Z}^n$, $p_1,\dots, p_{d …
- 1,502
38
votes
Accepted
Does every polyomino tile R^n for some n?
A positive answer to this question has just appeared in the arXiv:
Tiling with arbitrary tiles;
Vytautas Gruslys, Imre Leader, Ta Sheng Tan;
http://arxiv.org/abs/1505.03697
- 1,502
4
votes
A rational polytope that is not a 01-polytope?
Every simplicial polytope is rational, hence there are infinitely many rational polytopes in any fixed dimension. In contrast, there are finitely many 0/1 polytopes, since they cannot have more than $ …
- 1,502
2
votes
n-dimensional Delaunay Triangulation of Lattices
The answer to 2 and 1 is "No".
For (2), observe that a positive answer here would imply all Delaunay simplices to be unimodular (i.e., have volume equal to $1/n!$ times the volume of a fundamental p …
- 1,502
5
votes
Which (semi)regular polyhedra are combinations of two others?
I think the whole list of Gjiergji (and lightly more, see below) follows from Wythoffian operations. For the cube-octahedron family, for example, consider the following diagram:
The polyhedron along a …
- 1,502