منابع مشابه
Regular Maps - Combinatorial Objects Relating Different Fields of Mathematics
Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familiar examples of regular maps. The great dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps ...
متن کاملCombinatorial maps
The classical approach to maps, as surveyed by Coxeter and Moser (“Generators and Relations for Discrete Groups,” Springer-Verlag, 1980), is by cell decomposition of a surface. A more recent approach, by way of graph embedding schemes, is taken by Edmonds (Notices Amer. Math. Sot. 7 (1960), 646), Tutte (Canad. J. Math. 31 (5) (1979), 986-1004), and others. Our intention is to formulate a purely...
متن کاملRegular Surfaces and Regular Maps
A regular surface is a closed genus g surface defined as the tubular neighbourhood of the edge graph of a regular map. A regular map is a family of disc type polygons glued together to form a 2-manifold which is flag transitive. The visualization of this highly symmetric surface is an intriguing and challenging problem. Unlike regular maps, regular surfaces can always be visualized as 3D embedd...
متن کاملRegular Homomorphisms and Regular Maps
Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...
متن کاملIntroduction to Combinatorial Maps
Preface Maps as a mathematical main topic arose probably from the four color problem[Ore1] and the more general map coloring problem[Rin1] in the mid of the nineteenth century. I could not list even main references on them because it is well known for mathematicians and beyond the scope of this lecture notes. Here, I only intend to present a comprehensive theory of combinatorial maps as a rigor...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1983
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90053-9