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19 votes
3 answers
2k views

Guises of the Stasheff polytopes, associahedra for the Coxeter $A_n$ root system?

Richard Stanley keeps a famous running compilation of different guises of the celebrated Catalan numbers. The number of vertices of the associahedron is one instantiation among the multitude, and the ...
Tom Copeland's user avatar
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19 votes
2 answers
1k views

About a Delzant polytope. (In particular dodecahedron)

Hi. I have a question. Definition. Delzant polytope $P$ is a rational convex simple polytope with the smooth condition. Here, "smooth" means that for each vertex $v$, the $n$ edges containing $v$ ...
Yunhyung Cho's user avatar
  • 1,037
3 votes
0 answers
102 views

The ring generated by a convex polytope and its faces

Let $V=\Bbb R^n$. Morelli defined the (commutative unital) ring $L(V)$ to be the additive group generated by the indicator functions of convex polytopes in $V$ with multiplication induced by Minkowski ...
Avi Steiner's user avatar
  • 3,079