Steinhaus' lattice point problem for polyhedra
Volume 146 / 2017
Colloquium Mathematicum 146 (2017), 123-128
MSC: Primary 52C07; Secondary 11P21.
DOI: 10.4064/cm6213-5-2016
Published online: 23 September 2016
Abstract
It is proved that for every $d$-dimensional polyhedron $\varPi $ in ${\mathbb {R}}^d, \,d\ge 2$, with volume $n+\alpha ,\,|\alpha | \lt 1$, there is a congruent copy of $\varPi $ that contains exactly $n$ lattice points.
