Towards an empirical relation between the elementary polygonal circuit area and the topological form index, l, in the polyhedra and 2- and 3-dimensional structures

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Volumn 54, Issue 2, 2005, Pages 313-330

  Bucknum, Michael J ^a   Castro, Eduardo A ^b  

^a GEORGIA COLLEGE AND STATE UNIVERSITY   (United States)

^b INSTITUTO DE INVESTIGACIONES FISICOQUÍMICAS TEÓRICAS Y APLICADAS INIFTA   (Argentina)

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EID: 29344471270     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

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2. M. Henle, A Combinatorial Introduction to Topology. 1st Edition, W.H. Freeman and Company, San Francisco, CA, 1979, p.9.
3. A.F. Wells, The Geometrical Basis of Crystal Chemistry: (a) Part 1, A.F. Wells (1954) Acta Cryst., 7, 535.
4. (b) Part 2, A.F. Wells (1954) Acta Cryst., 7, 545.
5. (c) Part 3, A.F. Wells (1954) Acta Cryst., 7, 842.
6. (d) Part 4, A.F. Wells (1954) Acta Cryst., 7, 849.
7. (e) Part 5, A.F. Wells (1955) Acta Cryst., 8, 32 .
8. (f) Part 6, A.F. Wells (1956) Acta Cryst., 9, 23.
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10. (h) Part 8, A.F. Wells (1965) Acta Cryst., 18, 894.
11. (i) Part 9, A.F. Wells (1968) Acta Cryst., B24, 50.
12. (j) Part 10, A.F. Wells (1969) Acta Cryst., B25, 1711.
13. (k) Part 11, A.F. Wells (1912) Acta Cryst., B28, 711.
14. (l) Part 12, A.F. Wells (1976) Acta Cryst., B32, 2619.
15. (m) A.F. Wells, Three Dimensional Nets and Polyhedra. 1st Edition, John Wiley and Sons Inc., New York, 1977.
16. (n) A.F. Wells, Further Studies of Three-dimensional Nets, American Crystallographic Association, Monograph Number 8, 1st Edition, American Crystallographic Association Press, 1979. Note that unfortunately the author could not locate direct references to the work of Schläfli in topology, the references to Wells are indirect but refer to Schläfli's work.
17. (a) M. Wenninger, Dual Models, 1st edition, Cambridge University Press, 1983.
18. (b) P.J. Frederico, "Descartes on Polyhedra: A Study of the De Solidorum Elementis", appearing in Sources in the History of Mathematics and Physical Sciences 4, 1st edition, Springer-Verlag, 1982.
19. M.J. Bucknum, Carbon, 35(1), 1, (1997).
20. The fundamental polyhedra metric, the correspondence principle, the morphological principle, all used to derive the 2D and 3D metrics and determine the data in Table 1; and the Wells coincidences and Wells conjecture; have all been named to honor Professor A.F. Wells who was at the University of Connecticut for some years, where he established himself as a master of applied topology and derived more than 100 novel networks.
21. U. Müller, Inorganic Structural Chemistry, 2nd edition, John Wiley and Sons Inc., New York, 1992.
22. F.A. Bannister, Zeit. f. Krist., 96, 201, (1937).
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24. (b) J. Waser and E.D. McClanahan, J. Chem. Phys., 19, 413, (1951).
25. M.J. Bucknum, Chemistry Preprint Server, CPS: physchem/0011002, November 2, 2000.
26. M.J. Bucknum, Chemistry Preprint Server, CPS: physchem/0101003, January 31, 2001.