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 $v$ form an element of $GL(n,\mathbb{Z})$, where $n$ is a dimension of $P$.

(If you wonder why this condition is called smooth, See Fulton. Introduction to toric variety chap I)

My question is as follow.

Can dodecahedron be the Delzant polytope? I mean, is there a symplectic toric manifold whose moment map image is combinatorially equivalent to a dodecahedron?

Delzant's classfication theorem of compact symplectic toric manifold is surely very strong. But I think it is very hard to check whether the given polytope (having many faces) is of Delzant type or not. If you know any reference of give me any comment, I really appriciate for your help.

Thank you.

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 $v$ form an element of $SL(n,\mathbb{Z})$, where $n$ is a dimension of $P$.

(If you wonder why this condition is called smooth, See Fulton. Introduction to toric variety chap I)

My question is as follow.

Can dodecahedron be the Delzant polytope? I mean, is there a symplectic toric manifold whose moment map image is combinatorially equivalent to a dodecahedron?

Delzant's classfication theorem of compact symplectic toric manifold is surely very strong. But I think it is very hard to check whether the given polytope (having many faces) is of Delzant type or not. If you know any reference of give me any comment, I really appriciate for your help.

Thank you.

Hi. I have a stupid 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 $v$ form an element of $GL(n,\mathbb{Z})$, where $n$ is a dimension of $P$.

(If you wonder why this condition is called smooth, See Fulton. Introduction to toric variety chap I)

My question is as follow.

Can dodecahedron be the Delzant polytope? I mean, is there a symplectic toric manifold whose moment map image is combinatorially equivalent to a dodecahedron?

Delzant's classfication theorem of compact symplectic toric manifold is surely very strong. But I think it is very hard to check whether the given polytope (having many faces) is of Delzant type or not. If you know any reference of give me any comment, I really appriciate for your help.

Thank you.

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 $v$ form an element of $GL(n,\mathbb{Z})$, where $n$ is a dimension of $P$.

(If you wonder why this condition is called smooth, See Fulton. Introduction to toric variety chap I)

My question is as follow.

Can dodecahedron be the Delzant polytope? I mean, is there a symplectic toric manifold whose moment map image is combinatorially equivalent to a dodecahedron?

Delzant's classfication theorem of compact symplectic toric manifold is surely very strong. But I think it is very hard to check whether the given polytope (having many faces) is of Delzant type or not. If you know any reference of give me any comment, I really appriciate for your help.

Thank you.