# Questions tagged [triangulations]

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59 questions
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### Minimum weight triangulation of lattice points in a circle

Let $r$ be a natural number, and consider the $\mathbb{Z}^2$ lattice points $S$ inside or on the circle $C$ of radius $r$ centered on the origin. Let $P$ be the convex hull of $S$; so $P$ is inscribed ...
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### Are there non-cuspy triangulations of smooth manifolds?

In (as it turned out my misunderstanding of) the literature, a "smooth triangulation" seems to mean: a homeomorphism from a simplicial complex, such that on each simplex the map can be extended to a ...
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### Are there invariants of cell complexes similar to the Euler characteristic?

The Euler characteristic is an invariant (under homeomorphism) of manifolds that can be computed from a cellulation by (weighted) counting of different kinds of objects, namely \chi=\...
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### Edgebreaker algorithm over 2-manifolds

Suppose I triangulate a 2-manifold and make a dual pseudograph over it. If I do the Edgebreaker compression algorithm over this graph to generate a spanning tree, can exist an edge with three or more ...
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### Combinatorial curvature of real projective plane

There is a notion of combinatorial curvature due to Forman, see here (published paper) or here (preprint). I checked for a couple of small triangulations of $\mathbb{RP}^2$ (6-vertex, 7-vertex, 9-...
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### Finite union of closed convex sets is triangulable?

I posted this question on math.stackexchange.com, but didn't get an answer. Let $A_1, \ldots, A_k \subseteq \mathbb{R}^n$ be closed convex sets. Is the union $\bigcup_{i=1}^k A_i$ triangulable, that ...
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### Eberhard-type theorems for Fisk triangulations?

A triangulation of a surface is called a Fisk triangulation if the degree of all but two vertices is even, and these two exceptional vertices of odd degree are neighbors. I would like to know what ...
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### regular triangulations of the product of two simplices

Is description of all regular triangluations of $\Delta^n\times \Delta^k$ known? (Regular triangulations are those which correspond to vertices of Gelfand--Kapranov--Zelevinsky secondary polytope, or, ...
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