2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134884The aim of this paper is to provide the sufficient condition for a mass distribution in R^d to admit an equipartition with a collection of hyperplanes some of which are parallel. The results extend the previously obtained results for the equipartitions with non-parallel hyperplanes.Extended version with some new result and a little bit of motivation addedCombinatoricsAlgebraic Topologytext