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Results tagged with polytopes
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user 468
1
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Build a topological polytope with a specified CW-structure
There is a canonical thing to do if you have a lattice quotient of weak order on the symmetric group. Namely, you take the Coxeter fan (which has one maximal cone for each element of $S_n$) and you g …
- 6,327
5
votes
Build a topological polytope with a specified CW-structure
Once you note (as Forcey and Springfield do) that the cycle graph on $n$ vertices sits between the complete graph on $n$ vertices and the path on $n$ vertices, you get a sequence of maps of polytopes of …
- 6,327
1
vote
What can be said about number-theoretic properties of the solid angle measures of polytopal ...
$S_n$ acts on the set of cones, and preserves the solid angle measure. If you consider the $n!$ rotations of the cone by elements of $S_n$, and except on the union of some hyperplanes, the number of …
- 6,327