Skip to main content
SpringerLink
Log in

Counting symmetric and near-symmetric fullerene patches

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

We establish an exact method for drawing fullerene patches in the hexagonal tessellation of the plane. Using these embeddings, we then provide a closed form equation for the total number of symmetric and near-symmetric fullerene patches, up to isomorphism. The function depends only on parameters of the boundary code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. P. Bonsma, F. Breuer, Finding fullerene patches in polynomial time. in ISAAC 2009, vol 5878, LNCS, pp. 750–759 (2009)

  2. G. Brinkmann, A.W.M. Dress, PentHex puzzles: A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math. 21, 473–480 (1998)

    Article  Google Scholar 

  3. G. Brinkmann, N. Van Cleemput, Classification and generation of nanocones. Discrete Appl. Math. 159, 1528–1539 (2011)

    Article  Google Scholar 

  4. M. Deza, P.W. Fowler, V. Grishukin, Allowed boundary sequences for fused polycyclic patches and related algorithmic problems. J. Chem. Inf. Comput. Sci. 41, 300–308 (2011)

    Article  Google Scholar 

  5. C. Graves, J. McLoud-Mann, Side lengths of pseudoconvex fullerene patches. Ars Math. Contemp. 5, 291–302 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Texas at Tyler, Tyler, TX, 75799, USA

    Christina Graves & Stephen J. Graves

Authors
  1. Christina Graves
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen J. Graves
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christina Graves.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Graves, C., Graves, S.J. Counting symmetric and near-symmetric fullerene patches. J Math Chem 52, 2423–2441 (2014). https://doi.org/10.1007/s10910-014-0393-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-014-0393-2

Keywords

Search

Navigation