## On extraction of parallelotopes.(English)Zbl 1311.52014

Summary: A parallelotope is a convex polytope which fills the space facet to facet by its translation copies without intersecting by inner points. Consider the parallelotopes $$P$$ and $$Q$$. If there exists a direction $$\mathbf {v}$$ for which $$P \oplus \lambda \mathbf {v} = Q$$, where $$\oplus$$ denotes the Minkowski sum then $$Q$$ is called the extraction of $$P$$.
In this paper, we investigate when the extraction of a paralleotope is a parallelotope, too.

### MSC:

 52B11 $$n$$-dimensional polytopes

### Keywords:

extraction of parallelotopes; convex polytope