TL;DR
This paper surveys recent developments in combinatorial tilings of Euclidean and spherical spaces by polytopes, and discusses open problems to guide future research in the field.
Contribution
It provides a comprehensive overview of key progress and highlights open problems in combinatorial space tiling, including some new insights.
Findings
Summarizes main developments in combinatorial space tiling
Identifies open problems in Euclidean and spherical tilings
Highlights both old and new challenges in the field
Abstract
The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and some old open problems in this area.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Cellular Automata and Applications · graph theory and CDMA systems