# Integer decomposition of smooth polytopes

From Egres Open

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

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