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Abstract
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A parallelotope
is called
free
along a line
of the ambient
space if the Minkowski sum of
with a segment of the line
is a parallelotope. We prove that the Voronoi conjecture is true for a free
parallelotope along
and its projection
along the line
if each
4-belt of
has either 0
or 4 facets parallel to .
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Keywords
Voronoi's conjecture, parallelotope, free parallelotope
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Mathematical Subject Classification 2010
Primary: 52B11, 52C22
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Milestones
Received: 26 December 2017
Revised: 25 February 2021
Accepted: 12 March 2021
Published: 23 June 2021
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