Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)

Australian Journal of Chemistry

Volumn 56, Issue 10, 2003, Pages 981-1000

  Hyde, Stephen T ^a   Larsson, Ann Kristin ^a   Di Matteo, Tiziana ^a   Ramsden, Stuart ^a   Robins, Vanessa ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

LIQUID CRYSTALS; POLYMERS;

MODULAR GROUP STRUCTURE;

COLLOIDS;

EID: 0141892822     PISSN: 00049425     EISSN: None     Source Type: Journal    
DOI: 10.1071/CH03191     Document Type: Conference Paper

References (43)

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2. F. Klein, R. Fricke, Vorlesungen der Theorie der elliptischem Modulfunktionen, Bd. 1 [reprint 1966 (Johnson: New York, NY; Teubner: Stuttgart)]. We hasten to point out that we came to this reference circuitously. Klein's image was first encountered in a brilliantly accessible recent book: D. Mumford, C. Series, D. Wright, Indra's Pearls. The Vision of Felix Klein 2002 (Cambridge University Press: Cambridge).
3. J. H. Conway, in Groups, Combinatorics and Geometry - London Mathematical Society Lecture Note Series 1992 (Cambridge University Press: Cambridge). See also: J. H. Conway, D. H. Huson, Struct. Chem. 2002, 13, 247.
4. J. H. Conway, in Groups, Combinatorics and Geometry - London Mathematical Society Lecture Note Series 1992 (Cambridge University Press: Cambridge). See also: J. H. Conway, D. H. Huson, Struct. Chem. 2002, 13, 247.
5. See: D. Wells, The Penguin Dictionary of Curious and Interesting Geometry 1991 (Penguir: London); originally from H. Meschkowski, Unsolved and Unsolvable Problems in Geometry 1966 (Oliver & Boyd: London).
6. See: D. Wells, The Penguin Dictionary of Curious and Interesting Geometry 1991 (Penguir: London); originally from H. Meschkowski, Unsolved and Unsolvable Problems in Geometry 1966 (Oliver & Boyd: London).
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9. The notion of 'greater' or 'lesser' symmetry refers to the area of the fundamental domain, which scales with the absolute magnitude of the orbifold characteristic (or 'cost'), computed readily from the Conway orbifold symbol (ref. [2]).
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12. See, for examples: (a) A. F. Wells, Three-Dimensional Nets and Polyhedra 1977 (John Wiley: New York, NY). (b) M. O'Keeffe, B. G. Hyde, Crystal Structures. I. Patterns and Symmetry 1996 (Mineralogical Society of America: Washington, DC), (c) M. O'Keeffe, M. Eddaoudi, H. Li, T. Reineke, O. M. Yaghi, J. Solid State Chem. 2000, 152, 3.
13. See, for examples: (a) A. F. Wells, Three-Dimensional Nets and Polyhedra 1977 (John Wiley: New York, NY). (b) M. O'Keeffe, B. G. Hyde, Crystal Structures. I. Patterns and Symmetry 1996 (Mineralogical Society of America: Washington, DC), (c) M. O'Keeffe, M. Eddaoudi, H. Li, T. Reineke, O. M. Yaghi, J. Solid State Chem. 2000, 152, 3.
14. See, for examples: (a) A. F. Wells, Three-Dimensional Nets and Polyhedra 1977 (John Wiley: New York, NY). (b) M. O'Keeffe, B. G. Hyde, Crystal Structures. I. Patterns and Symmetry 1996 (Mineralogical Society of America: Washington, DC), (c) M. O'Keeffe, M. Eddaoudi, H. Li, T. Reineke, O. M. Yaghi, J. Solid State Chem. 2000, 152, 3.
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43. www.cs.ubc.ca/nest/Imager/contributions/scharein/KnotPlot.html.