Three-periodic tilings and nets: face-transitive tilings and edge-transitive nets revisited

被引：56

作者：

Delgado-Friedrichs, Olaf ^{[1
]}

O'Keeffe, Michael ^{[1
]}

机构：

[1] Arizona State Univ, Dept Chem & Biochem, Tempe, AZ 85287 USA

来源：

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES | 2007年 / 63卷

关键词：

D O I：

10.1107/S0108767307022283

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

Systematic generation of face-transitive tilings by size of Delaney-Dress symbol has recovered by dualization all the edge-transitive nets previously described and has led to the discovery of six new binodal edge-transitive nets which are described and illustrated.

引用

页码：344 / 347

页数：4

共 16 条

[1] The 3-regular nets with four and six vertices per unit cell [J].

Bader, M ;

Klee, WE ;

Thimm, G .

ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 1997, 212 (08) :553-558

[2] Topological relations between three-dimensional periodic nets. I. Uninodal nets [J].

Blatov, Vladislav A. .

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 2007, 63 :329-343

[3]

Delaney M. S., 1980, MATCH-COMMUN MATH CO, V9, P73

[4] What do we know about three-periodic nets? [J].

Delgado-Friedrichs, O ;

Foster, MD ;

O'Keeffe, M ;

Proserpio, DM ;

Treacy, MMJ ;

Yaghi, OM .

JOURNAL OF SOLID STATE CHEMISTRY, 2005, 178 (08) :2533-2554

[5] Identification of and symmetry computation for crystal nets [J].

Delgado-Friedrichs, O ;

O'Keeffe, M .

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 2003, 59 :351-360

[6] Recognition of flat orbifolds and the classification of tilings in R3 [J].

Delgado-Friedrichs, O .

DISCRETE & COMPUTATIONAL GEOMETRY, 2001, 26 (04) :549-571

[7] Three-periodic nets and tilings: edge-transitive binodal structures [J].

Delgado-Friedrichs, Olaf ;

O'Keeffe, Michael ;

Yaghi, Omar M. .

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 2006, 62 :350-355

[8] THE CLASSIFICATION OF FACE-TRANSITIVE PERIODIC 3-DIMENSIONAL TILINGS [J].

DRESS, AWM ;

HUSON, DH ;

MOLNAR, E .

ACTA CRYSTALLOGRAPHICA SECTION A, 1993, 49 :806-817

[9] PRESENTATIONS OF DISCRETE-GROUPS, ACTING ON SIMPLY CONNECTED MANIFOLDS, IN TERMS OF PARAMETRIZED SYSTEMS OF COXETER MATRICES - A SYSTEMATIC-APPROACH [J].

DRESS, AWM .

ADVANCES IN MATHEMATICS, 1987, 63 (02) :196-212

[10]

DRESS AWM, 1984, SLN, V1172, P56

← 1 2 →