4-regular vertex-transitive tilings of E3

被引：32

作者：

Friedrichs, OD ^{[1
]}

Huson, DH

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[2] Princeton Univ, Princeton, NJ 08544 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2000年 / 24卷 / 2-3期

关键词：

Crystal Structure; Topological Type; Tiling Theory; Combinatorial Tiling;

D O I：

10.1007/s004540010035

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

There exist precisely 149 topological types of semipolytopal tile-transitive tilings of E-3 by "extetrahedra" (obtained from tetrahedra by introducing certain new vertices of degree 2). Dualization gives rise to 149 types of 4-regular vertex-transitive tilings. The 4-coordinated networks carried by these tilings are closely related to crystal structures such as zeolites or diamond. These results are obtained using "combinatorial tiling theory".

引用

页码：279 / 292

页数：14

共 28 条

[1] CONWAY JH, 1999, UNPUB ORBIFOLD 2 DIM
[2] CONWAY JH, 1992, LONDON MATH SOC LECT, V165, P438
[3] CONWAY JH, 1999, UNPUB 3 DIMENSIONAL
[4] Danzer L., 1983, STRUCTURAL TOPOLOGY, V8, P3
[5] DELGADO O, 1994, THESIS BIELEFELD U
[6] Dolbilin N.P., 1997, PERIOD MATH HUNG, V34, P57
[7] THE CLASSIFICATION OF FACE-TRANSITIVE PERIODIC 3-DIMENSIONAL TILINGS
DRESS, AWM
HUSON, DH
MOLNAR, E
[J]. ACTA CRYSTALLOGRAPHICA SECTION A, 1993, 49 : 806 - 817
[8] PRESENTATIONS OF DISCRETE-GROUPS, ACTING ON SIMPLY CONNECTED MANIFOLDS, IN TERMS OF PARAMETRIZED SYSTEMS OF COXETER MATRICES - A SYSTEMATIC-APPROACH
DRESS, AWM
[J]. ADVANCES IN MATHEMATICS, 1987, 63 (02) : 196 - 212
[9] DRESS AWM, 1984, ALGEBR TOPOL, V1172, P56
[10] 3-DIMENSIONAL ALPHA-SHAPES
EDELSBRUNNER, H
MUCKE, EP
[J]. ACM TRANSACTIONS ON GRAPHICS, 1994, 13 (01): : 43 - 72

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