Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices: Polytopes in Hypercubes and Zn̳

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Imperial College Press, 2004 - Всего страниц: 175
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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.
 

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Содержание

Graphs and their Scaleisometric Embedding
1
from lattices Chapters 3 7 11 consider graphs in Rn Finally chapters
2
Embedding of Fullerenes
25
Regular Tilings and Honeycombs
35
Semiregular Polyhedra and Relatives of Prisms and Antiprisms
43
Truncation Capping and Chamfering
53
Semiregular and Regularfaced npolytopes n 4
71
Plane Tilings
83
Lattices Bilattices and Tiles
107
Small Polyhedra
115
Bifaced Polyhedra
119
Special tlgraphs
137
Some Generalization of iiembedding
153
Bibliography
163
Index
171
Авторские права

Uniform Partitions of 3space and Relatives
99

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