Vol. 10, No. 2, 2021

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Voronoi conjecture for special free parallelotopes

Viacheslav Grishukhin

Vol. 10 (2021), No. 2, 83–94
Abstract

A parallelotope P is called free along a line l of the ambient space if the Minkowski sum of P with a segment of the line l is a parallelotope. We prove that the Voronoi conjecture is true for a free parallelotope P along l and its projection along the line l if each 4-belt of P has either 0 or 4 facets parallel to l.

Keywords
Voronoi's conjecture, parallelotope, free parallelotope
Mathematical Subject Classification 2010
Primary: 52B11, 52C22
Milestones
Received: 26 December 2017
Revised: 25 February 2021
Accepted: 12 March 2021
Published: 23 June 2021
Authors
Viacheslav Grishukhin
Central Institute of Economics and Mathematics RAS
Russian Academy of Sciences
Moscow
Russia