## Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin
Nill, Andreas Paffenholz, Günter Rote, Francisco Santos, and Hal
Schenck:

# Finitely many smooth `d`-polytopes with `n` lattice
points

*Israel Journal of Mathematics* **207** (2015), 301–329.
doi:10.1007/s11856-015-1175-7,
arXiv:1010.3887 [math.CO].
### Abstract

We prove that for fixed `d` and `n`, there are only finitely
many smooth `d`-dimensional polytopes which contain `n` lattice
points. As a consequence in algebraic geometry, we obtain that for fixed
`n`, there are only finitely many embeddings of Q-factorial
toric varieties into `n`-dimensional projective
space P^{n} that are induced by a complete
linear system. We also enumerate all smooth 3-polytopes with at most 12
lattice points.
Last update: August 15, 2017.