Open AccessOn parallelotope configuration
Author(s) -
Attila Végh
Publication year - 2020
Publication title -
gradus
Language(s) - English
Resource type - Journals
ISSN - 2064-8014
DOI - 10.47833/2020.3.csc.002
Subject(s) - plane (geometry) , line (geometry) , connection (principal bundle) , polytope , regular polygon , translation (biology) , point (geometry) , facet (psychology) , combinatorics , geometry , computer science , mathematics , topology (electrical circuits) , physics , psychology , social psychology , biochemistry , chemistry , personality , big five personality traits , messenger rna , gene
The parallelotope P is a convex polytope which fills the spacefacet to facet by its translation copies without intersecting by in-ner points. A plane configuration is a system ofppoints andgstraight lines arranged in a plane in such a way that every pointof the system is incident with a fixed numberγof straight lines ofthe system and every straight line of the system is incident witha fixed numberπof points of the system. In this paper we exam-ine the connection of 3-dimensional parallelotopes and point-lineconfigurations in the plane and we generalize the concept of theconfiguration to describe all parallelotopes, this way we define theparallelotope configuration (p-configuration).