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Lattice Delone simplices with super-exponential volume

by Santos, F., Schürmann, A., Vallentin, F..

Series: 2005-34, Preprints

52B20 Lattice polytopes (including relations with commutative algebra and algebraic geometry)
52C22 Tilings in $n$ dimensions
11H99 None of the above, but in this section

In this short note we give a construction of an infinite series of Delone simplices whose relative volume grows super-exponentially with their dimension. This dramatically improves the previous best lower bound, which was linear.

Delone, simplex, volume, bounds