Timeline for Are simplicial polytopes a dense set?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| S Sep 16, 2022 at 13:50 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
corrected spelling in title
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| Sep 16, 2022 at 12:14 | review | Suggested edits | |||
| S Sep 16, 2022 at 13:50 | |||||
| Sep 15, 2022 at 9:40 | history | edited | user467453 | CC BY-SA 4.0 |
deleted 76 characters in body
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| Sep 15, 2022 at 9:32 | answer | added | Roland Bacher | timeline score: 1 | |
| Sep 15, 2022 at 9:15 | comment | added | user467453 | I am sorry for my earlier mistake. I was confused. Thanks a ton! | |
| Sep 15, 2022 at 8:24 | comment | added | Pietro Majer | The approximation you want is very easy then: take the convex hull of a finite $\epsilon$-net $S$ of the compact convex set $K\subset \mathbb R^d$, with the additional property that no $(d+1)$-subset of $S$ is affinely dependent (which is true for a dense open set in $(\mathbb R^d)^{|S|}$ ). Then $\text{co}(S)$ is a simplicial polytope whose Hausdorff distance from $K$ is not larger than $\epsilon$ . | |
| Sep 15, 2022 at 8:13 | comment | added | Pietro Majer | Sorry, I still don't get the definition you are referring to, even checking the wikipedia link. Isn't for you 1) A 2D convex polytope just a convex polygon? 2) A facet of a polygon just an edge, which is a 1D simplex? | |
| Sep 15, 2022 at 7:50 | comment | added | user467453 | No, only triangles: en.wikipedia.org/wiki/Simplicial_polytope If I had to prove the statement, I would try to prove it for polytopes and then show that simplicial polytopes lie dense in the polytopes, but again that cannot work for $d=2$. I rather not, however, since I assume this should be known. | |
| Sep 15, 2022 at 7:47 | comment | added | Pietro Majer | I'd say the answer is yes for any $d\ge0$. Why $d=2$ is special? Aren't then simplicial polytopes just the convex polygons? | |
| S Sep 15, 2022 at 6:24 | review | First questions | |||
| Sep 15, 2022 at 6:43 | |||||
| S Sep 15, 2022 at 6:24 | history | asked | user467453 | CC BY-SA 4.0 |