Timeline for About a Delzant polytope. (In particular dodecahedron)
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 16, 2022 at 10:50 | comment | added | Francisco Santos | According to grdb.co.uk/search/toricf3c there are 416 reflexive $3$-polytopes of volume 20 and with 12 boundary points. You need to find one whose boundary can be triangulated as an icosahedron with the triangulation being regular (aka coherent, aka projective). Among the 416 examples I wouldd expect there to be at least one... As an example, the fan in Panov's answer below comes from triangulating the boundary of a cube octahedron, which is the reflexive polytope with ID 12645 in grdb.co.uk/search/toricf3c | |
| Nov 11, 2015 at 14:08 | answer | added | Elisa Prato | timeline score: 7 | |
| Apr 13, 2011 at 20:13 | history | edited | Dmitri Panov | CC BY-SA 3.0 |
edited body; edited tags
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| Apr 13, 2011 at 20:12 | answer | added | Dmitri Panov | timeline score: 4 | |
| Apr 2, 2011 at 8:28 | history | edited | Gil Kalai | CC BY-SA 2.5 |
edited tags; deleted 6 characters in body
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| Mar 15, 2011 at 22:50 | comment | added | Tracy Hall | The obvious first thing to try is a rational pyritohedron, but that fails: at one of the eight vertices with threefold rotational symmetry, the adjacent edges lie along directions which are the even permutations of $(p^2, -pq, q^2)$ for positive coprime integers $p \gt q$, giving $(p^3+q^3)^2$ for a determinant, rather than $1$. | |
| Mar 15, 2011 at 21:46 | comment | added | André Henriques | As far as the classification of toric symplectic manifolds is concerned, the property "having a Delzant polytope of the combinatorial type of the regular dodecahedron" seems unmotivated. Nevertheless, it's a nice question. | |
| Mar 15, 2011 at 20:53 | history | asked | Yunhyung Cho | CC BY-SA 2.5 |