A while ago I heard that there was no known triangulation of the Grassmannian of 3-planes in 6-space. To believe a statement like that, you have to be a little bit ungenerous abou …

Given 4 points $A$, $B$, $C$ and $D$ in general position in the euclidean plane, is it possible to determine from the 6 distances $AB$, $BC$, $CD$, $AD$, $AC$ and, $BD$ alone, whet …

A friend and I were reading up on the classification of compact surfaces when we realized that the minimal number of triangles in a triangulation of the sphere, torus, and projecti …

Let $M$ be a smooth closed manifold and $T$ be a triangulation of $M$. Endow each simplex of $T$ with the Euclidean metric making it a regular simplex; this gives a piecewise Eucli …

I am sorry but I am reposting this question because I wasn't logged in when I first asked it. Ian Agol has produced a method to build an ideal layered triangulation of a hyperboli …

[Edit: I had a mistake in the numerology (took d=6,5 instead d=5,4). Edit: I mistakingly identified my mistake, it is 6,5 but I got the indices shifted by one.] Background: Polygo …

Hyperbolic plane has a beautiful triangulation by congruent hyperbolic triangles where all the vertices of the triangulation have degree 7, this is of course not possible in the eu …

This is my first question on mathoverflow! It relates to a project I'm undertaking with a student. Work by Tamura (extending results by Luo and Stong) shows that for any closed 3- …

Does every polyhedron in $\mathbb{R}^3$ with $n$ triangular facets have a topological triangulation with complexity $O(n)$? Suppose $P$ is a non-convex polyhedron in $\mathbb{R}^3 …

Work by Tamura (extending results by Luo and Stong) shows the following. Theorem: For any closed 3-manifold $M$ and any rational number $4.5 < r < 6$ there is a triangula …

Let us call a finite union $P$ of $n$-dimensional compact convex polytopes in $\mathbb{R}^n$ a non-convex polytope. Recall that a dissection of $P$ is a finite collection $T$ of $n …

I heard this really neat elementary proof of the "Gauss-Bonnet Theorem" : Let $S$ be a surface embedded in $\mathbb{R}^3$. Now take a triangulation of that surface, and approximat …

I'm looking for an algorithm that is easy to implement in practice (resulting in small amount of code), preferably incremental. As far as I know, the biggest problem with increment …