On extraction of parallelotopes. (English) Zbl 1311.52014

Végh, A.

Stud. Univ. Žilina, Math. Ser. 26, No. 1, 49-54 (2014).

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