Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn

AvMichel-marie Deza,Viacheslav Grishukhin

Inbunden, Engelska, 2004

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Beskrivning

This monograph identifies polytopes that are “combinatorially ℓ1-embeddable”, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to “ℓ2-prominent” affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability — the main unifying question, to which those lists are subjected — is presented with the minimum of technicalities.

Produktinformation

Utgivningsdatum:2004-02-16
Mått:152 x 236 x 15 mm
Vikt:406 g
Format:Inbunden
Språk:Engelska
Antal sidor:188
Förlag:Imperial College Press
ISBN:9781860944215

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

Recensioner i media

"The authors give concise and independent presentations of most of the topics and the readers of different backgounds will be able to browse or study those chapters which are of interest for them. The presentation allows the book to serve a variety of needs." Mathematical Reviews

Innehållsförteckning

Introduction: Graphs and Their Scale-Isometric Embedding - An Example: Embedding of Fullerenes - Regular Tilings and Honeycombs - Semi-regular Polyhedra and Relatives of Prisms and Antiprisms - Truncation, Capping and Chamfering - 92 Regular-faced (not Semi-regular) Polyhedra - Semi-regular and Regular-faced n-Polytopes, n 4 - Polycycles and Other Chemically Relevant Graphs - Plano Tilings - Uniform; Partitions of 3-Space and Relatives - Lattices, Bi-lattices and Tiles - Small Polyhedra - Bifaced Polyhedra - Special 1-graphs - Some Generalization of 1-embedding