Tagged Questions

16 views

Graph of polytope and hyperplane

Suppose that $P$ is a compact and convex polytope in $R^d$ and let $G$ be the graph of $P$ ($V(G)$ are the vertices of $P$ and $E(G)$ are the $1$-dimensional faces - for example polyedral graphs are ...
69 views

Describe conv(A∪B) [closed]

Let A and B be congruent non-intersecting regular icosahedra, with B a translated copy of A. Arrange A in some convenient position (say with the line through the top and bottom vertices vertical), and ...
115 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 ...
93 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 ...
252 views

Average degree of convex hull vertices in a Delaunay triangulation

Let $P \subset \mathbb{R}^2$. The boundary of $DT(P)$, the Delaunay triangulation of the point set $P$, is $conv(P)$. It is also known that the average degree of the vertices of $DT(P)$ is $\lt 6$. ...
218 views

Accesible Area of Discrete Geometry for Undergraduate Research [closed]

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 ...