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Original Articles

The Geometry of Regular Repeating Pattern

Pages 1-62 | Published online: 13 Jan 2009

REFERENCES

  • Woods , H. J. 1935 . Journal of the Textile Institute, Transactions , 26 : T197
  • Woods , H. J. 1935 . Journal of the Textile Institute, Transactions , 26 : T293
  • Woods , H. J. 1935 . Journal of the Textile Institute. , 26 : T341 Transactions
  • Woods , H. J. 1936 . Journal of the Textile Institute, Transactions , 27 : T305
  • Shepard , A. 1948 . “The Symmetry of Abstract Design with Special Reference to Ceramic Decoration”, Contribution no. 47 , Publication no. 574 Washington : Carnegie Institute of Washington .
  • Crowe , D. W. 1971 . Journal of Geometry , 1 : 169
  • Crowe , D. W. 1975 . Historia Mathemauca , 2 : 253
  • Crowe , D. W. 1980 . Ba Shiru: Journal of African Languages and Literature , 11 ( 1 ) : 57
  • Crowe , D. W. 1982 . “The Geometry of African Art. Part 3. The Smoking Pipes of Begho” . In “The Geometric Vein: The Coxeter Festschrift” Edited by: Davis , C. , Grunbaum , B. and Sherk , F. A. 177 New York : Springer .
  • Crowc , D. W. 1986 . “The Mosaic Patterns of H. J. Woods” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 407 New York : Pergamon .
  • Crowe , D. W. and Washburn , D. K. 1985 . Algebras, Groups and Geometries , 3 ( 2 ) : 263
  • Crowe , D. W. and Washburn , D. K. 1987 . “Flow Charts as an Aid to the Symmetry Classification of Patterned Design” . In “Material Anthropology: Contemporary Approaches to Material Culture” Edited by: Reynolds , B. and Stott , M. A. 69 Lanham, Maryland : University Press of America .
  • Washburn , D. K. 1977 . “A Symmetry Analysis of Upper Gila Area Ceramic Design” . In Papers of the Peabody Museum of Archaeology and Ethnology Vol. 68 , Cambridge, Mass. : Harvard University .
  • Washburn , D. K. 1977 . “A Symmetry Classification of Pueblo Ceramic Design” . In “Discovering Past Behaviour: Experiments in the Archaeology of the American Southwest” Edited by: Grebtnger , P. 101 New York : Gordon Breach .
  • Washburn , D. K. 1980 . “The Mexican Connection: Cylinder Jars from the Valley of Oaxaca” . In “New Frontiers in the Archaeology and Ethnohistory of the Greater Southwest” Edited by: Riley , C. L. and Hendrick , B. C. Vol. 72 , 70 Transactions of the Illinois State Academy of Science . No. 4
  • Washburn , D. K. 1983 . “Towards a Theory of Structural Style ” . In Art”, in “Structure and Cognition in Art” Edited by: Washburn , D. K. 1 Cambridge, Mass. : Cambridge University Press .
  • Washburn , D. K. 1983 . “Symmetry Analysis of Ceramic Design: Two Tests of the Method on Neolithic Material from Greece and the Aegean” . In “Structure and Cognition in Art” Edited by: Washburn , D. K. 138 Cambridge, Mass. : Cambridge University Press .
  • Washburn , D. K. 1986 . Empirical Studies of the Arts , 4 ( 1 ) : 19
  • Washburn , D. K. 1986 . “Pattern Symmetry and Coloured Repetition ” . In Cultural Contexts”, in “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 767 New York : Pergamon .
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 43 New York : Freeman .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” Seattle : University of Washington Press . Chp. 4
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 42 New York : Freeman .
  • Buerger , M. J. and Lukesh , J. S. 1937 . Technology Review , 39 : 338
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 ( 6 ) : 439
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 43 New York : Freeman .
  • Mamedov , K. S. 1986 . “Crystallographic Patterns” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 511 New York : Pergamon .
  • Jones , O. 1982 . “The Grammar of Ornament” New York : Van Nostrand Reinhold . (reprinted from the 1856 edition).
  • Crowe , D. W. 1986 . “The Mosaic Patterns of H. J. Woods” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 407 New York : Pergamon .
  • Durant , S. 1986 . “Ornament. A Survey of Decoration Since 1830” London : Macdonald . Chp. 1
  • Racinet , A. 1869 . “L'Ornement Polychrome” Firmin Didot Freres. Paris .
  • Meyer , F. S. 1894 . “Handbook of Ornament: A Grammar of Art Industrial and Architectural”, , 4th ed. New York : Hessling and Spielmayer . Reprinted by Dover, New York, 1957, and as “Meyer's Handbook of Ornament”, Omega, London, 1987
  • Speltz , A. 1914 . “The Coloured Ornament of All Historical Styles” . In “Antiquity” Leipzig : K. F. Koehlers Antiquarium . vol. 1
  • Speltz , A. 1915 . “The Coloured Ornament of All Historical Styles” . In “Middle Ages” Leipzig : A. Schumann . vol. 2
  • Speltz , A. “The Coloured Ornament of All Historical Styles” . In “Modern Times” Leipzig, n.d. : K. F. Koehlers Antiquarium . vol. 3
  • Bourgoin , J. 1879 . “Les Elements de L'art Arabe: Le Trait des Entrelacs” Firmin-Didot Paris . Reprinted as: “Arabic Geometrical Pattern and Design”, Dover, New York, 1973
  • Audsley , W. and Audsley , G. 1968 . “Outlines of Ornaments in the Leading Styles”, Scribner and Welford, London, 1882. New edition: “Designs and Patterns from Historic Ornament” New York : Dover .
  • Kelley , C. F. and Mowll , W. L. 1912 . “A Test-Book of Design” Boston : Houghton Mifflin .
  • Lewis , A. B. 1925 . “Decorative Art of New Guinea: Incised Designs” , Anthropological Design Series No. 4, Field Museum of Natural History, Chicago,.Reprinted as: “Decorative Art of New Guinea”. Dover, New York, 1973
  • Fenn , A. 1930 . “Abstract Design” London : Batsford .
  • Edwards , E. B. 1932 . “Dynamarhythmic Design” New York : Century . Reprinted as: “Pattern and Design with Dynamic Symmetry”, Dover, New York 1967
  • Christie , A. H. 1929 . “Pattern Design. An Introduction to the Study of Formal Ornament”, , 2nd ed. Oxford : Clarendon Press . Reprinted as: “Pattern Design”, Dover, New York, 1969
  • Bossert , H. T. 1928 . “Farbige Dekorationen. Beispiele dekorativer Wandmalerei von Altertum bis zur Mitte des 19. Jahrunderts” Berlin : Wasmuth . English translation: “An Encyclopaedia of Colour Decoration”, Gollancz, London, 1928
  • Dye , D. S. 1937 . “A Grammar of Chinese Lattice” Boston : Harvard University Press . New edition; “Chinese Lattice Designs”, Dover, New York 1974
  • Bain , G. 1951 . “Celtic Art. The Methods of Construction” Glasgow : W. Maclellan . Reprinted: Dover. New York,1973
  • Bodrogi , T. 1959 . “Oceanian Art” Budapest : Corvlna .
  • Proctor , R. M. 1969 . “The Principles of Pattern for Craftsmen and Designers” New York : Van Nostrand .
  • Ernst , B. 1976 . “The Magic Mirror of M. C. Escher” New York : Random House .
  • Hornung , C. P. 1975 . “Allover Patterns for Designers and Craftsmen” New York : Dover .
  • Albam , K. , Smith , J. M. , Steele , S. and Walker , D. 1974 . “The Language of Pattern” New York : Harper and Row .
  • Menten , T. 1975 . “Japanese Border Designs” New York : Dover .
  • Hann , M. A. and Thomson , G. M. 1990 . “The Printed Calicos of Manchester, circa 1900”, Vol. 1 in the Crown House Collection of Textile Documents Whaley Bridge, Derbyshire, England : Crown House Publishing .
  • Durant , S. 1986 . “Ornament. A Survey of Decoration Since 1830” London : Macdonald . Chp. 1
  • Meyer , F. S. 1894 . “A Handbook of Ornament” 3 London : Batsford . Reprinted: “Meyer's Handbook of Ornament”, Omega, London, 1987, (a) Introduction; (b)p.
  • Woods , H. J. 1935 . Journal of the Textile Institute, Transactions , 26 : T293
  • Stephenson , C. and Suddards , F. 1897 . “A Textbook Dealing With Ornamental Design for Woven Fabrics” London : Methuen . Chps. 2-5
  • Day , L. F. 1903 . “Pattern Design” London : Batsford . Chps. 2-6
  • Christie , A. H. 1929 . “Pattern Design. An Introduction to the Study of Formal Ornament”, , 2nd ed. 59 Oxford : Clarendon Press . First published as “Traditional Methods of Pattern Designing”, Clarendon Press, Oxford. 1910. Reprinted as “Pattern Design”, Dover, New York, 1969, (a)Chp. 9; (b)p.
  • Shubnikov , A. V. and Koptsik , V. A. 1974 . “Symmetry in Science and Art” New York : Plenum Press .
  • Coxeter , H. S. M. 1961 . “Introduction to Geometry” New York : Wiley . Chp. 3
  • Jeger , M. 1966 . “Transformation Geometry” New York : Wiley . Chps. 1-6
  • Guggenheimer , H. W. 1967 . “Plane Geometry and Its Groups” San Francisco : Holden-Day . Chp. 2
  • Yale , P. B. 1968 . “Geometry and Symmetry” San Francisco : Holden-Day . Chp. 2
  • Gans , D. 1969 . “Transformations and Geometries” New York : Appleton-Century-Croft . Chp. 2
  • Ewald , G. 1971 . “Geometry: An Introduction” Belmont, CA : Wadsworth . Chp. 1
  • Dodge , C. W. 1972 . “Euclidean Geometry and Transformations” Reading, MA : Addison-Wesley .
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 ( 6 ) : 439
  • Hargittai , I. 1986 . “Symmetry Through the Eyes of a Chemist” New York : VCH Publishers . Chps.2 and 8
  • Martin , G. E. 1982 . “Transformation Geometry. An Introduction to Symmetry” New York : Springer-Verlag .
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 27 New York : Freeman .
  • Campbell , P. J. 1989 . “The Geometry of Decoration on Prehistoric Pueblo Pottery From Starkweather Ruin” . In “Symmetry 2: Unifying Human Understanding” Edited by: Hargittai , I. 731 New York : Pergamon Press .
  • Schattschneider , D. 1986 . “In Black and White: How to Create Perfectly Coloured Symmetric Patterns” Edited by: Hargittai , I. New York : Pergamon Press . (a) p. 673; (b) p. 675; (c) p. 676; (d) p. 677
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions” 11 Cambridge, Mass. : M. I. T. Press . (paperback edition), p.
  • Schattschneider , D. 1986 . “In Black and White: How to Create Perfectly Coloured Symmetric Patterns” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 678 New York : Pergamon Press .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” 255 Seattle : University of Washington Press .
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 55 New York : Freeman .
  • Fedorov , E. S. “Elements of the Theory of Figures”, (in Russian), Imp. Acad. Sci., St. Petersburg, 1885 (cited by Grunbaum and Shephard, reference 75)
  • Fedorov , E. S. 1891 . “Symmetry in the Plane” (in Russian) ” . In Zapiski Rus. Mineralog. Obscestva, Ser. 2 Vol. 28 , 345 (cited by Grunbaum and Shephard, reference 75)
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” 56 New York : Freeman .
  • Polya , G. 1924 . Zeitschrift fur Kristallographie , 60 : 278
  • Niggli , P. 1924 . Zeitschrift fur Kristallographie , 60 : 283
  • Niggli , P. 1926 . Zeitschnft fur Kristallographie. , 63 : 255
  • Speiser , A. 1927 . “Die Theorie der Gruppen von Endlicher Ordnung” Berlin : Springer .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture” 4 Seattle : University of Washington Press .
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 ( 6 ) : 439
  • Birkhoff , G. D. 1933 . “Aesthetic Measure” Cambridge, MA : Harvard University Press .
  • Crowe , D. W. 1986 . “The Mosaic Patterns of H. J. Woods” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 407 New York : Pergamon .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture” 9 Seattle : University of Washington Press .
  • Buerger , M. J. and Lukesh , J. S. 1937 . Technology Review , 39 ( 8 ) : 338
  • Shepard , A. 1948 . “The Symmetry of Abstract Design with Special Reference to Ceramic Decoration”, Contribution no. 47 , Publication no. 574 Washington : Carnegie Institute of Washington .
  • Weyl , H. 1952 . “Symmetry” Princeton : Princeton University Press .
  • Shubnikov , A. V. and Koptsik , V. A. 1974 . “Symmetry in Science and Art” New York : Plenum Press .
  • Walker , T. and Padwick , R. 1977 . “Pattern: Its Structure and Geometry” Sunderland Arts Centre, England : Ceolfrith Press .
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 ( 6 ) : 439
  • Schattschneider , D. 1986 . “In Black and White: How to Create Perfectly Coloured Symmetric Patterns” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 673 New York : Pergamon Press .
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions” Cambridge, Mass. : M. I. T. Press . (paperback edition)
  • Crowe , D. W. 1980 . Ba Shiru , 11 ( 1 ) : 57
  • Crowe , D. W. and Washburn , D. K. 1986 . “Flow Charts as an Aid to the Symmetry Classification of Patterned Design” . In “Material Anthropology: Contemporary Approaches to Material Culture” Edited by: Reynolds , B. and Stott , M. 69 Lanham, Maryland : University Press of America .
  • Rose , B. I. and Stafford , R. D. 1981 . American. Mathematical Monthly , 88 : 59
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” New York : Freeman .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture, Theory and Practice of Plane Pattern Analysis” Seattle : University of Washington Press .
  • Hargittai , I. , ed. 1986 . “Symmetry: Unifying Human Understanding” New York : Pergamon .
  • Hargittai , I. , ed. 1989 . “Symmetry 2: Unifying Human Understanding” New York : Pergamon .
  • Boas , F. 1927 . “Primitive Art” Aschehoug, Osl o,(reprint: Dover, New York, 1955), (a) p. 32; (b) p. 33
  • Holm , B. 1965 . “Northwest Coast Indian Art: An Analysis of Form”. University of Washington Press Seattle
  • Levi-Strauss , C. 1974 . “Tristes Tropiques” New York : Atheneum .
  • Critchlow , K. 1976 . “Islamic Patterns” New York : Schocken Books .
  • Glassie , H. 1975 . “Folk Housing in Middle Virginia” Knoxville : University of Tennessee Press .
  • Brainerd , G. W. 1942 . American Antiquity , 8 ( 2 ) : 164
  • Stewart , J. D. 1980 . Current Anthropology , 21 ( 4 ) : 539
  • Muller , E. 1944 . “Gruppentheoretische und Strukturanalytische Untersuchungen der Maurischen Ornamente aus der Alhambra in Granada” University of Zurich . D. thesis.
  • Grunbaum , B. , Grunbaum , Z. and Shephard , G. C. 1986 . “Symmetry ” . In Moorish and Other Ornaments”, in “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 641 New York : Pergamon .
  • Shepard , A. 1948 . “The Symmetry of Abstract Design with Special Reference to Ceramic Decoration”, Contribution no. 47 , Publication no. 574 Washington : Carnegie Institute of Washington .
  • Shepard , A. 1956 . “Ceramics for the Archaeologist” 263 – 305 . Washington : Carnegie Institute of Washington, Publication no 609 .
  • MacGillavry , C. H. 1965 . “Symmetry Aspects of M. C. Escher's Periodic Drawings” Utrecht : published for the International Union of Crystallography by A Oasthoek's Uitgeversmaatschappy . Reprinted as “Fantasy and Symmetry: The Periodic Drawings of M. C. Escher”, Abrams, New York, 1976
  • Locher , J. L. 1982 . “M. C. Escher: His Life and Complete Graphic Work” 162 New York : Abrams .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” 11 Seattle : University of Washington Press .
  • Washburn , D. K. 1986 . “Pattern Symmetry and Coloured Repetition ” . In Cultural Contexts”, in “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 767 New York : Pergamon .
  • Crowe , D. W. 1971 . Journal of Geometry , 1 : 169
  • Crowe , D. W. 1975 . Historia Mathematics , 2 : 253
  • Crowe , D. W. 1982 . “The Geometry of African Art. Part 3. The Smoking Pipes of Begho” . In “The Geometric Vein: The Coxeter Festschrift” Edited by: Davis , C. , Grunbaum , B. and Sherk , F. A. 177 New York : Springer .
  • Zaslow , B. and Dittert , A. E. 1977 . “The Pattern Technology of Hohokam, in Pattern Mathematics and Archaeology” , Anthropological Research Papers No. 2 Tempe, Arizona : Arizona State University .
  • Ascher , M. and Ascher , R. 1981 . “Code of the Quipu: A Study in Media, Mathematics, and Culture” 54 – 57 . Ann Arbor : TheUniversity of Michigan Press .
  • Van Esterik , P. 1979 . Journal of Anthropological Research , 35 ( 4 ) : 495
  • Kent , K. P. 1983 . “Temporal Shifts ” . In the Structure of Tradition: South-western Textile Design”, in “Structure and Cognition in Art” Edited by: Washburn , D. K. 113 Cambridge, Mass. : Cambridge University Press .
  • Washburn , D. K. 1977 . “A Symmetry Analysis of Upper Gila Area Ceramic Design” . In Papers of the Peabody Museum of Archaeology and Ethnology, vol. 68 Cambridge, Mass. : Harvard University .
  • Washburn , D. K. and Matson , R. G. 1984 . “Use of Multidimensional Scaling to Display Sensitivity of Symmetry Analysis of Patterned Design to Spatial and Chronological Change: Examples from Anasazi Prehistory” . In “Decoding Prehistoric Ceramics” Edited by: Nelson , B. 75 Carbondale : Southern Illinois University Press .
  • Washburn , D. K. 1983 . “Symmetry Analysis of Ceramic Design: Two Tests of the Method on Neolithic Material from Greece and the Aegean” . In “Structure and Cognition in Art” Edited by: Washburn , D. K. 138 Cambridge, Mass. : Cambridge University Press .
  • Washburn , D. K. 1986 . Empirical Studies of the Arts , 4 ( 1 ) : 1986
  • Campbell , P. J. 1989 . “The Geometry of Decoration on Prehistoric Pueblo Pottery from Starkweather Ruin” . In “Symmetry 2: Unifying Human Understanding” Edited by: Hargittai , I. 731 New York : Pergamon Press .
  • Washburn , D. K. 1977 . “A Symmetry Analysis of Upper Gila Area Ceramic Design” . In Papers of the Peabody Museum of Archaeology and Ethnology, vol. 68 173 Cambridge, Mass. : Harvard University .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” 57 Seattle : University of Washington Press . (a) Appendix 2; (b)p.
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions” Cambridge, Mass. : M. I. T. Press. . (paperback edition), (a) p. 126; (b) p. 148
  • Woods , H. J. 1935 . Journal of the Textile Institute, Transactions , 26 : T197
  • Crowe , D. W. 1987 . UMAP Journal , 8 ( 3 ) : 207
  • Budden , F. J. 1972 . “The Fascination of Groups” London : Cambridge University Press .
  • Cadwell , J. H. 1966 . “Topics in Recreational Mathematics” London : Cambridge University Press .
  • Coxeter , H. S. M. 1961 . “Introduction to Geometry” New York : Wiley . sections 3-7
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns. An introduction to Symmetry in Two Dimensions” Cambridge, Mass. : M. I. T. Press . (paperback edition), sections 12-19
  • Crowe , D. W. and Washburn , D. K. 1987 . “Flowcharts as an Aid to the Symmetry Classification of Patterned Design” . In “Material Anthropology: Contemporary Approaches to Material Culture” Edited by: Reynolds , B. and Stott , M. A. 69 Lanham, Maryland : University Press of America .
  • Rose , B. I. and Stafford , R. D. 1981 . American Mathematical Monthly , 88 : 59
  • Martin , G. E. 1982 . “Transformation Geometry. An Introduction to Symmetry” New York : Springer-Verlag .
  • Schwarzenberger , R. L. E. 1974 . Mathematical Gazette , 58 : 123
  • Schattschneider , D. “In Black and White: How to Create Perfectly Coloured Symmetric Patterns” . In “Symmetry: Unifying Human Understanding” Edited by: Hargittai , I. 673 New York : Pergamon .
  • Grunbaum , B. and Shephard , G. C. “Tilings and Patterns” New York : Freeman and Company .
  • Nowacki , W. 1972 . Zeitschrift fur Kristallographie , 135 : 145
  • Coxeter , H. S.M. and Moser , W. O.J. 1972 . “Generators and Relations for Discrete Groups” , 3rd edition Berlin : Springer .
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 : 439
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” p.58 Seattle : University of Washington Press .
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions” Cambridge, Mass. : M.I.T. Press . (paperback edition), Appendix.
  • Birkhoff , G. D. 1933 . “Aesthetic Measure” Cambridge, Mass. : Harvard University Press .
  • Bradley , A. D. 1933 . “The Geometry of Repeating Design and Geometry of Design for High Schools” New York : Columbia University, Teachers College Press .
  • Buerger , M. J. 1956 . “Elementary Crystallography” New York : Wiley .
  • MacGillavry , C. H. 1976 . “Symmetry Aspects of M.C. Escher's Periodic Drawings” New York : Abrams . Oosthoek, Utrecht, 1965. Reprinted as: “Fantasy and Symmetry. The Periodic Drawings of M.C. Escher”
  • Burckhardt , J. J. 1966 . “Die Bewegungsgruppen der Kristallographie” , 2nd edition Basel : Birkhauser .
  • Coxeter , H. S.M. and Moser , W. O.J. 1972 . “Generators and Relations for Discrete Groups” , 3rd edition Berlin : Springer .
  • Loeb , A. L. 1971 . “Colour and Symmetry” New York : Wiley .
  • Shubnikov , A. V. and Koptsik , V. A. 1974 . “Symmetry in Science and Art” New York : Plenum Press .
  • Schwarzenberger , R. L.E. 1974 . The Mathematical Gazette , 58 : 123
  • Schattschneider , D. 1978 . American Mathematical Monthly , 85 : 439
  • Stevens , P. S. 1984 . “Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions” Cambridge, Mass. : M.I.T. Press . (paperback edition).
  • Crowe , D. W. and Washburn , D. K. 1987 . “Flow Charts as an Aid to the Symmetry Classification of Patterned Design”, in “Material Anthropology: Contemporary Approaches to Material Culture” Edited by: Reynolds , B. and Stott , M. A. p.69 Lanham, Maryland : University Press of America .
  • Christie , A. H. 1969 . “Pattern Design” New York : Dover . Chp.10.
  • Woods , H. J. 1936 . Journal of the Textile Institute , 27 : T305 Transactions
  • Gombrich , E. H. 1979 . “The Sense of Order. A Study in the Psychology of Decorative Art” p.89 London : Phaidon .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” p.68 Seattle : University of Washington Press . (a) Chp.3; (b)
  • Belov , N. V. 1964 . “On One-Dimensional Infinite Crystallographic Groups”, in “Coloured Symmetry” Edited by: Shubnikov , A. V. and Belov , N. V. p.225 New York : Pergamon .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture, Theory and Practice of Plane Pattern Analysis” Seattle : University of Washington Press . (a) p.69; (b) p.70.
  • Belov , N. V. and Tarkhova , T. N. 1964 . “Dichromatic Plane Groups”, in “Coloured Symmetry” Edited by: Shubnikov , A. V. and Belov , N. V. p.211 New York : Pergamon .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” Seattle : University of Washington Press . (a) p.70; (b) Chp.5.
  • Woods , H. J. 1936 . Journal of the Textile Institute , 27 : T305 Transactions
  • Jarratt , J. D. and Schwarzenberger , R. L.E. 1981 . Utilitas Mathematica , 19 : 295
  • Wieting , T. W. 1981 . “The Mathematical Theory of Plane Chromatic Ornaments” New York : Marcel Dekker .
  • Schwarzenberger , R. L.E. Mathematical Gazette , 58 123
  • Grunbaum , B. and Shephard , G. C. 1987 . “Tilings and Patterns” New York : Freeman .
  • Washburn , D. K. and Crowe , D. W. 1988 . “Symmetries of Culture. Theory and Practice of Plane Pattern Analysis” p.24 Seattle : University of Washington Press .

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