Monatshefte für Mathematik

, Volume 86, Issue 3, pp 185-188

First online:

On multiple space subdivisions by zonotopes

  • H. GroemerAffiliated withDepartment of Mathematics, The University of Arizona

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It is shown that everyd-dimensional zonotopeC whose vertices satisfy a certain rationality condition has the following property: There exist a positive integerk and a sequenceC 1,C 2,... of translates ofC such that every point ofd-space that is not a boundary point of someC i is in exactlyk of the setsC 1,C 2,...