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Results tagged with polyhedra
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user 468
5
votes
Build a topological polytope with a specified CW-structure
Edited to add: I now think the answer below is completely wrong. The three-dimensional cyclohedron has 12 facets, while the three-dimensional polytope the OP is looking for should have 14. This is t …
- 6,302
2
votes
Accepted
How can pushing a vertex in a polytope lead to merging facets?
What happens as you push $v$, is that you can break a face into two. Start with a cube in $\mathbb R^3$, choose a vertex, and start to push it into the interior of the cube. Each of the three facets …
- 6,302
1
vote
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 …
- 6,302
1
vote
Growth polynomial of the Associahedron graph ? (Is it approximately Gaussian ?)
Let's consider the associahedron whose vertices are triangulations of an $n$-gon. Sleator, Tarjan, and Thurston (Rotation distance, triangulations, and hyperbolic geometry, JAMS, 1988)
give a simple a …
- 6,302