Timeline for Does the edge-graph of a centrally symmetric polytope determine which vertices are antipodal?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2023 at 18:30 | vote | accept | M. Winter | ||
| Feb 21, 2023 at 13:39 | comment | added | Brendan McKay | Yes, that clarifies it, thanks. | |
| Feb 21, 2023 at 11:19 | history | edited | David E Speyer | CC BY-SA 4.0 |
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| Feb 21, 2023 at 11:08 | history | edited | David E Speyer | CC BY-SA 4.0 |
added 35 characters in body
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| Feb 21, 2023 at 11:07 | comment | added | David E Speyer | Wait, the second sentence says " I will give an example of a centrally symmetric polytope in $\mathbb{R}^4$ with $12$ vertices where there is a symmetry of the edge graph interchanging two non-antipodal vertices." This is right; the symmetry interchanges $f(\gamma)$ and $f(\pi-\gamma)$, which are not antipodal, and fixes the others. (I'm going to add "and fixes the other ten vertices" for clarity, though.) | |
| Feb 21, 2023 at 7:35 | comment | added | Brendan McKay | You prove that there is a symmetry that doesn't preserve antipodal pairs, which indeed answers the OP. It isn't what your second sentence says though (which is satisfied by my cube example in a comment to Dima's answer that does not answer the OP). I'm only questioning your wording. | |
| Feb 21, 2023 at 3:42 | history | answered | David E Speyer | CC BY-SA 4.0 |