THE DIMENSIONALITY OF SUPRAMOLECULAR COMPOUNDS

Г.В. Жижин

Abstract


The geometric features of supramolecular compounds known to be important for biological systems are considered to show that the dimensionality of the compounds is higher than three.

Keywords


supramolecular compounds, dimensionality, polytope, hemoglobin, chlorophyll

References


Zhizhin GV. Мир 4D. [Word 4D]. Saint Petersburg: Politekhnika-Servis; 2014, p. 243. (In Russ.)

Zhizhin GV. [On higher dimensions in Nature]. Biosfera. 2014;(4):313-8. (In Russ.)

Len Zh.-M. Supramolekuliarnaya Khimiya: Kontseptsii i Perspektivy. Novosibirsk: Nauka, 1998. (In Russ., translated from: Lehn J-M. Supramolecular Chemistry: Concepts and Perspectives. Weinheim: VCH, 1995.)

Riemann B. Sochineniya [Works]. Moscow: OGIZ; 1948. (In Russ., translated from German.)

Rokhlin VA, Fuks DV. Nachal’niy Kurs Topologii. Geomеtrocheskiye Glavy. [Basic Course of Topology. Geometric Chapters]. Moscow: Nauka; 1977. (In Russ.)

Stid DV, Etvud DL. Supramolekuliarnaya Khimiya. Moscow: Akademkniga; 2007. (In Russ., translated from Steed JV, Atwood JL. Supramolecular Chemistry. Chichester: John Wiley & Sons; 2000.)

Coxeter HSM. Regular Polytopes. New York: Makmillan; 1963.

Grunbaum B. Con vex Polytopes. London: Springer; 1967.

Lehn J-M. La Chimie Supramoleculaire. La Recherche. 1981;(127):1213.

MacMullen P, Shephard GC. Convex Polytopes and Upper Bound Conjecture. Cambridge: Cambridge University Press; 1971.

Poincare A. Analysis Situs. J de Ecole Polyt. 1895;(1):1-121.

Shevchenko VYa, Zhizhin GV, Mackay A. On the structures of the quasicrystals in the high dimension space. In: Diudea MV, Nagy CL, eds. Diamods and Related Nanostructures. Dordrecht, Heidelberg, New York, London: Springer; 2013: 311-20.

Stringhem WI. Regular figures in d-dimensional space. Amer J Math. 1880;(3):1-14.

Weyl H. Elementare theory der konvexon polyeder. Comm Math Helvetici. 1935;(7):290- 306.

Zhizhin GV, Khalaj Z, Diudea MV. Geometrical and topological dimensions of the diamonds. In: Ashrafi AR, Diudea MV, eds. Distance, Symmetry and Topology in Carbon Nanomaterials. Dordrecht, Heidelberg, New York, London: Springer; 2015 (accepted for publication).




DOI: http://dx.doi.org/10.24855/biosfera.v7i2.55

© ФОНД НАУЧНЫХ ИССЛЕДОВАНИЙ "XXI ВЕК"