The Seventeen Two-Dimensional Space-Group Symmetries in Hungarian Needlework lstvan Hargittai' University of Connecticut. Storrs, CT 06268 Gyorgyi Lengyel Council of Popular Arts and Crafts, Budapest, Hungary We have recently demonstrated all seven one-dimensional space-group symmetries through ~xamplesfound in Hungarian needlew~rk.~ The utility of these analogies is obvious in teaching crystallography and symmetry. Several colleagues have urged us to compile and communicate a similar system for the 17 two-dimensional space groups. The two-dimensional space groups are more complex than the one-dimensional ones, but they are also considerably closer to the three-dimensional space-groups of the crystals. As is well known, there are 230 of the latter, hut unfortunately no needlework analogies can be presented for them. Seventeen Hungarian needleworks are shown below together with corresponding systems of an asymmetric motif,
the hlack triangle. Some of the most important s>mmetry elements are HISO indicated on them. More detailed drsrrintions can be found in books, including Buerger's classic, " ~ 1 ementary CrystalIography,"3 which has in some ways inspired the present work. A brief description of the 17 pieces of needlework is given in the captions.
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On leave (1983t85)from the Hungarian Academy of Sciences: mailing address: Budapest. P.O. Box 117, Hungary, H-1431. EDUC., 61, 1033 (1984). Hargittai, I., and Lengyel, Gy., J. CHEM. Buerger. M. J., "Elementary Crystallography." Wiley. New York, 1963.
Figure 1. Needlework designs corresponding to the firstsix two-dimensional space-group symmetries: p l andp4: Patterns of indigodyed decorations on textiles for clothing. Seiiye. Baranya County, 1899. p2: i n d i g d y e d decoration with palmette motif far curtains. Currently a very papular pattern. p3 andp6: Decorations with characteristic bird motifs from peasant vests. Northern Hungary. pm:Decoration with tulip motif for table-cloth. Crossstitched needlework from the turn of the century. Volume 62 Number 1 January 1985
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F i g m 2. Needlework designs corresponding to the last 11 twodimttnsionai space-group symmetries. pmm2: Bed-sheet border decoration with pomegranatemotif. Northwest Hungary. 19th century. p4mm: Pillow-slip decaatian with stars.Cross-stitched neediwak. Transylvania, 19th century. p6mm. p3m1, and p31m: Decorations with characteristic bird motih from peasant vests. Nonhern Hungary. cm: Pillow-slip dewration wim peawck tail motif. Cross-stitched needlework. Much used throughout Hungary around the turn of the century. cmm2: 8Bd-sheet border decoration with cockscomb motif. Cross-stitched needlework. Samogy county. 19th century. pg: From a panern b w k of indigodyed decorations. Papa. Vesrprem county. 1856. pgg2: Children's bag decoration. Transylvania, turn of the century. pmg2: Pillowslip decoration with scrolling stem matif. Much used throughout Hungary around the turn of the century. p4gm: Blousearm embroidery. BBcs-Kiskun county, 19th century.
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