0
votes
1answer
26 views

The line between the centers of two k-simplices crosses through the centers of lower dimensional simplices

"The line between the centers of two k-simplices crosses through the centers of lower dimensional simplices." Is this always true? The barycentric centers are equidistant from the vertices. k=2 So ...
1
vote
0answers
44 views

A question about partitioning the unit cube into simplexes

Let $C$ be the unit cube in $\mathbb{R}^n$. I want to simplicize $C$ (i.e. partition it into simplexes), but I have to follow these two rules: I can't add any vertices to $C$. The vertices of each ...
2
votes
2answers
84 views

What is a good way to simplicize the integer lattice?

I have a function $f$ defined on the positive integer lattice in $\mathbb{R}^n$ (i.e. the vectors in $\mathbb{R}^n$ whose coordinates are all nonnegative integers). I want to extend the domain of $f$ ...
2
votes
1answer
73 views

Inner product between certain vectors on a simplex.

For $n\geq 2$, let $\Delta^n$ be a regular $n$-dimensional simplex in $\mathbb{R}^n$ centered at the origin ${\bf 0}$ and inscribed in the unit sphere $S^{n-1}$. Let ${\bf v}_0,{\bf v}_1,\ldots,{\bf ...
3
votes
2answers
206 views

Triangulate rectangular parallelepiped in $\mathbb{R}^{n}$

I need to triangulate the n-dimensioned rectangular parallelepiped in $\mathbb{R}^{n}$ into a set of $n$-simplices. Could you suggest me any known algorithm for that or maybe an extension of Delaunay ...
0
votes
1answer
159 views

Maximum number of simplexes given n-element point sets in the plane

Does anyone know if it has been proved what the maximum number of simplexes occurring in the plane is for a given value of $n$ points? I am interested in this question in relation to packing problems ...
1
vote
1answer
112 views

simplex and power set

I read the following: Let $M$ be a set. The simplex on $M$ is the set of all subsets of $M$; we denote this by $\Delta_M$. We will sometimes refer to the elements of $M$ as vertices of $\Delta_M$. A ...
1
vote
0answers
59 views

Valuations, simplicial complexes and arithmetics

I am currently working on an Introduction to geometric probability (Klein, Rota, 1997). This book is very stimulating, and I find myself toying with the subject, and a note in particular (pp 95-97 for ...