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
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
收藏
页码:1 / 17
页数:17
相关论文
共 16 条
[11]   CLUSTER APPROACH FOR QUASI-CRYSTALS [J].
JEONG, HC ;
STEINHARDT, PJ .
PHYSICAL REVIEW LETTERS, 1994, 73 (14) :1943-1946
[12]  
Penrose R., 1978, EUREKA, V39, P16
[13]   A NEW METHOD FOR GENERATION OF QUASI-PERIODIC STRUCTURES WITH N FOLD AXES - APPLICATION TO 5-FOLDS AND 7-FOLDS [J].
SASISEKHARAN, V .
PRAMANA, 1986, 26 (03) :L283-L293
[14]   QUASI-CRYSTALS - THE VIEW FROM LES-HOUCHES [J].
SENECHAL, M ;
TAYLOR, J .
MATHEMATICAL INTELLIGENCER, 1990, 12 (02) :54-64
[15]  
SENECHAL M, 1995, GEOMETRY QUASICRYSTA
[16]   THE STRUCTURE OF QUASI-CRYSTALS [J].
STEURER, W .
ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 1990, 190 (3-4) :179-234