Ten colours in quasiperiodic and regular hyperbolic tilings

被引：6

作者：

Lueck, Reinhard ^{[1
]}

Frettloeh, Dirk ^{[1
]}

机构：

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

来源：

ZEITSCHRIFT FUR KRISTALLOGRAPHIE | 2008年 / 223卷 / 11-12期

关键词：

Hyperbolic tilings; Regular tilings; Colour symmetry; Colour group;

D O I：

10.1524/zkri.2008.1059

中图分类号：

O7 [晶体学];

学科分类号：

0702 ; 070205 ; 0703 ; 080501 ;

摘要：

Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using combination of two-colour and five-colour symmetries. Here we present explicit constructions of several of the predicted colourings for the first time, and discuss them in contrast to already known colourings with ten colours.

引用

页码：782 / 784

页数：3

共 10 条

[1] Bravais colourings of planar modules with N-fold symmetry [J].

Baake, M ;

Grimm, U .

ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 2004, 219 (02) :72-80

[2] Combinatorial aspects of colour symmetries [J].

Baake, M .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (08) :2687-2698

[3]

BAAKE M, EUROP J COM IN PRESS

[4] Colorings of hyperbolic plane crystallographic patterns [J].

De Las Penas, Ma Louise Antonette N. ;

Felix, Rene P. ;

Laigo, Glenn R. .

ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 2006, 221 (10) :665-672

[5] Counting perfect colourings of plane regular tilings [J].

Frettloeh, Dirk .

ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 2008, 223 (11-12) :773-776

[6]

Grunbaum B., 1987, Tilings and Patterns

[7]

GUMMELT P, 1999, APERIODISCHE UBERDEC, P36

[8] 2-COLOR PENROSE TILING [J].

LI, XZ ;

DUBOIS, JM ;

KUO, KH .

PHILOSOPHICAL MAGAZINE LETTERS, 1994, 69 (02) :93-98

[9]

LUCK R, 2008, PHIL MAG IN PRESS

[10] COLOR SYMMETRY [J].

SCHWARZENBERGER, RLE .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1984, 16 (MAY) :209-&

← 1 →