Tagged Questions
3
votes
1answer
95 views
Can all convex polytopes be realized with vertices on surface of convex body?
Each convex polytope $P$ has a combinatorial type, its so-called face lattice. This lattice is just the poset of all faces of $P$ ordered by inclusion. Given one realization of such a combinatorial ...
2
votes
0answers
80 views
“Round” regions on surface of convex polytope
A convex $d$-polytope $P$ is the convex hull of finitely many points. Given such a polytope with $n \gg d$ vertices, I would like to prove that its surface has to be "round" in some region.
Let me ...
2
votes
0answers
172 views
Accesible Area of Discrete Geometry for Undergraduate Research
This summer I will have a chance to work on a 16-week summer research project under a professor in convex/discrete geometry. I'm a first-year student with a fairly good background for my age and I've ...
4
votes
3answers
120 views
What is the name of this property?
If there are 3 intervals, such that any 2 of them intersect, then all 3 of them intersect.
For any 4 disks, if any 3 of them have a non empty intersection, then all 4 of them have a common ...
1
vote
1answer
215 views
How close are star-convex sets to convex sets?
What interesting properties of convex sets are retained by star-convex sets?
