# Integer decomposition of smooth polytopes

Is it true that every smooth polytope has the integer decomposition property?

## Remarks

This question was asked by Tadao Oda [1], see also the survey of Gubeladze [2]. The conjecture has been verified for smooth polytopes containing at most 12 lattice points [3], and there is no known smooth polytope without a unimodular triangulation. For cases when a unimodular triangulation is known to exist, see [4].

## References

1. T. Oda, Problems on Minkowski sums of convex lattice polytopes, arXiv link
2. J. Gubeladze, Normal polytopes, manuscript
3. T. Bogart et al., Few smooth d-polytopes with n lattice points, arXiv link
4. C. Haase, A. Paffenholz, L.C. Piechnik, F. Santos, Existence of unimodular triangulations - positive results, arXiv link