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Rod tetrahedral structures based on polytope 240

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Abstract

Various Hopf fibrations of polytope 240 are obtained. Six rod structures consisting of tetrahedral atoms are derived by rolling a polytope 240 along three-dimensional Euclidean space E3 and simultaneous mapping to this space. The axes of these rod structures are the projections of the Hopf circles corresponding to different discrete fibrations of a polytope 240. Some of these structures were obtained previously by the method of modular design, but their relation to polytope 240 was not established. As was shown previously, fractal structures can be obtained on the basis of one of these rod structures and, in addition, the same rod structure, when consisting of water molecules, can be important in biological processes, as it stores elastic energy and can release it by a cooperative transition.

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Notes

  1. I.e., the one similar to a zigzag chain —C—C—C—C— along the direction < 110 > in the diamond structure.

  2. I.e., a chain similar to a —C—C—C—C— helix with the axis 41 or 43 along the direction < 100 > in the diamond structure.

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Acknowledgements

The author is grateful to N.A. Bulienkov for fruitful discussions.

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Authors and Affiliations

  1. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskii prosp. 31, Moscow, 119071, Russia

    E. A. Zheligovskaya

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  1. E. A. Zheligovskaya
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Being a single author of the paper, the author formulated the problem, solved it, prepared the draft of the paper (including figures), edited it, and, finally, approved the final manuscript.

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Correspondence to E. A. Zheligovskaya.

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Dedicated to Alan Mackay for his 95th anniversary

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Zheligovskaya, E.A. Rod tetrahedral structures based on polytope 240. Struct Chem 33, 237–245 (2022). https://doi.org/10.1007/s11224-021-01843-6

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  • DOI: https://doi.org/10.1007/s11224-021-01843-6

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