Timeline for An example of a "simple poset" which does not belong to a convex polytope
Current License: CC BY-SA 4.0
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| Sep 28, 2019 at 18:42 | comment | added | Joseph O'Rourke | Good point, @lambda. This is overkill, but: Theorem 47. $K_{m,n}$ is $d$-realizable if and only if $n = m = d \in \{1,2\}$. Espenschied, William Joshua. "Graphs of polytopes." PhD diss., University of Kansas, 2014. | |
| Sep 28, 2019 at 18:41 | comment | added | giulio bullsaver | Any kind of counterexample is appreciated, however I changed the question in such a way that this example no longer applies: the reason why K_{3,3} cannot be the 1-skeleton of a polytope is due to some combinatorical/topological obstruction, i.e. one cannot even find a poset with that 1-skeleton. I would like an example where a poset satisfies all the topological checks but a convex realisation its known to be impossible | |
| Sep 28, 2019 at 18:36 | comment | added | Ilya Bogdanov | @lambda Shouldn't a skeleton of 4-dimensional polytope be 4-connected, or at least have degrees not smaller than 4? | |
| Sep 28, 2019 at 18:31 | comment | added | lambda | The question didn't specify a 3-dimensional polytope. | |
| Sep 28, 2019 at 18:28 | vote | accept | giulio bullsaver | ||
| Sep 29, 2019 at 12:33 | |||||
| Sep 28, 2019 at 17:40 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 69 characters in body
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| Sep 28, 2019 at 17:33 | history | answered | Joseph O'Rourke | CC BY-SA 4.0 |