IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p1001-d279111.html
   My bibliography  Save this article

Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)

Author

Listed:
  • Garrett Sadler

    (Quantum Gravity Research, Topanga, CA 90290, USA)

  • Fang Fang

    (Quantum Gravity Research, Topanga, CA 90290, USA)

  • Richard Clawson

    (Quantum Gravity Research, Topanga, CA 90290, USA
    Faculty of Health, Engineering and Sciences, University of Southern Queensland, Toowoomba, QLD 4350, Australia)

  • Klee Irwin

    (Quantum Gravity Research, Topanga, CA 90290, USA)

Abstract

The Boerdijk–Coxeter helix is a helical structure of tetrahedra which possesses no non-trivial translational or rotational symmetries. In this document, we develop a procedure by which this structure is modified to obtain both translational and rotational (upon projection) symmetries along/about its central axis. We show by construction that a helix can be obtained whose shortest period is any whole number of tetrahedra greater than one except six, while a period of six necessarily entails a shorter period. We give explicit examples of two particular forms related to the pentagonal and icosahedral aggregates of tetrahedra as well as Buckminster Fuller’s “jitterbug transformation”.

Suggested Citation

  • Garrett Sadler & Fang Fang & Richard Clawson & Klee Irwin, 2019. "Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)," Mathematics, MDPI, vol. 7(10), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:1001-:d:279111
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/1001/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/1001/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:1001-:d:279111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.