Penrose tilings as coverings of congruent decagons

被引：186

作者：

Gummelt, P ^{[1
]}

机构：

[1] UNIV GREIFSWALD,FACHBEREICH MATH & INFORMAT,D-17489 GREIFSWALD,GERMANY

来源：

GEOMETRIAE DEDICATA | 1996年 / 62卷 / 01期

关键词：

tiling; Penrose tiling; aperiodic tile; quasicrystal;

D O I：

10.1007/bf00239998

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The open problem of tiling theory whether there is a single aperiodic two-dimensional prototile with corresponding matching rules, is answered for coverings instead of tilings. We introduce admissible overlaps for the regular decagon determining only nonperiodic coverings of the Euclidean plane which are equivalent to tilings by Robinson triangles. Our work is motivated by structural properties of quasicrystals.

引用

页码：1 / 17

页数：17

共 16 条

[1] APERIODIC TILES [J].

AMMANN, R ;

GRUNBAUM, B ;

SHEPHARD, GC .

DISCRETE & COMPUTATIONAL GEOMETRY, 1992, 8 (01) :1-25

[2] QUASI-PERIODIC TILINGS WITH TENFOLD SYMMETRY AND EQUIVALENCE WITH RESPECT TO LOCAL DERIVABILITY [J].

BAAKE, M ;

SCHLOTTMANN, M ;

JARVIS, PD .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (19) :4637-4654

[3] STRUCTURE MODEL OF THE AL-CU-CO DECAGONAL QUASI-CRYSTAL [J].

BURKOV, SE .

PHYSICAL REVIEW LETTERS, 1991, 67 (05) :614-617

[4]

BURKOV SE, 1992, J PHYS I, V2, P695, DOI 10.1051/jp1:1992160

[5]

DIVINCENZO D, 1991, DIRECTIONS CONDENSED, V11

[6]

Fujiwara T., 1990, QUASICRYSTALS

[7]

Gardner M., 1977, Scientific American, V236, P110, DOI DOI 10.1038/SCIENTIFICAMERICAN0177-110

[8]

Gr?nbaum B., 1987, TILINGS PATTERNS

[9]

Gummelt P, 1995, PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON QUASICRYSTALS, P84

[10]

JARIC MV, 1989, APERIODICITY ORDER, V1

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