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Lattice coverings by parallelotopes containing cube vertices
We investigate when a parallelotope containing vertices of the unit cube $Q_n=[0,1]^n$ covers $\Bbb R^n$ by integer translates. We prove the covering property for every parallelepiped containing five vertices of $Q_3$, and, in any dimension, for every parallelotope containing a facet of $Q_n$ and on
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