Vol. 10, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN (electronic): 2996-220X
ISSN (print): 2996-2196
Author Index
To Appear
 
Other MSP Journals
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