2023/01/05 by Plamen Dimitrov, Dimitrov, Plamen
Engineering · Materials Science · #20F55 (Primary) #51M20 (Secondary) #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2301.01880
openalex publication_date 2023/01/05 · openalex created_date 2023/01/08 · openalex updated_date 2026/07/28
This work presents the tessellations and polytopes from the perspective of both n-dimensional geometry and abstract symmetry groups. It starts with a brief introduction to the terminology and a short motivation. In the first part, it engages in the construction of all regular tessellations and polytopes of n dimensions and extends this to the study of their quasi-regular and uniform generalizations. In the second part, the symmetries of polytopes and tessellations are considered and the Coxeter groups and their associated root systems are introduced and classified. In the last part, the algorithms developed for this work are described and their results discussed.