Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)

Article


Sadler, Garrett, Fang, Fang, Clawson, Richard and Irwin, Klee. 2019. "Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)." Mathematics. 7 (10), pp. 1-18. https://doi.org/10.3390/math7101001
Article Title

Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)

ERA Journal ID213646
Article CategoryArticle
AuthorsSadler, Garrett (Author), Fang, Fang (Author), Clawson, Richard (Author) and Irwin, Klee (Author)
Journal TitleMathematics
Journal Citation7 (10), pp. 1-18
Article Number1001
Number of Pages18
Year2019
PublisherMDPI AG
Place of PublicationSwitzerland
ISSN2227-7390
Digital Object Identifier (DOI)https://doi.org/10.3390/math7101001
Web Address (URL)https://www.mdpi.com/2227-7390/7/10/1001
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'.

Keywordshelical structure of tetrahedra; boerdijk-coxeter helix; icosahedral aggregates of tetrahedra
ANZSRC Field of Research 2020499999. Other mathematical sciences not elsewhere classified
Byline AffiliationsQuantum Gravity Research, United States
University of Southern Queensland
Institution of OriginUniversity of Southern Queensland
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https://research.usq.edu.au/item/q7966/periodic-modification-of-the-boerdijk-coxeter-helix-tetrahelix

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