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Results tagged with polyhedra
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user 2233
1
vote
Testing whether two vertices are neighbours
You should first check that $v_i$ and $v_j$ are both vertices of $X$. Given the description $X = \{ x \in \mathbb{R}^k \, : \, A x \leq b \}$, this is easy.
Suppose that $A$ is an $m \times n$ mat …
- 32.1k
12
votes
Visibility of vertices in polyhedra
One can attempt to do the same thing in 3 dimensions, but somewhat surprisingly there exist polyhedra that cannot be decomposed into tetrahedra (without adding additional vertices). … See here, where they show that the problem of deciding if a 3-dimensional polyhedra can be decomposed into tetrahedra is NP-complete. The references in that paper might be helpful. …
- 32.1k
19
votes
Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all h...
The answer to the third question is no. This is a rather counter-intuitive discovery of Micha Perles from the sixties. See this paper of Ziegler, for a simpler construction and other pertinent infor …
- 32.1k