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Mellon
Mellon
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Let $P$ be a simple $3$-dimensional (and full-dimensional) lattice polytope such that every facet $F$ is a smooth polytope. Is then $P$ itself smooth?

EDIT: A full-dimensional lattice polytope $P$ is called smooth if its normal fan $\Sigma_P$ is smooth.

Let $P$ be a simple $3$-dimensional (and full-dimensional) lattice polytope such that every facet $F$ is a smooth polytope. Is then $P$ itself smooth?

Let $P$ be a simple $3$-dimensional (and full-dimensional) lattice polytope such that every facet $F$ is a smooth polytope. Is then $P$ itself smooth?

EDIT: A full-dimensional lattice polytope $P$ is called smooth if its normal fan $\Sigma_P$ is smooth.

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Mellon
Mellon
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  • 9

Simple polytope with smooth facets

Let $P$ be a simple $3$-dimensional (and full-dimensional) lattice polytope such that every facet $F$ is a smooth polytope. Is then $P$ itself smooth?