Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)

Sadler, Garrett and Fang, Fang and Clawson, Richard and Irwin, Klee (2019) Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix). Mathematics, 7 (10):1001. pp. 1-18.

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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'.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 - 31 Dec 2021)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 - 31 Dec 2021)
Date Deposited: 03 Aug 2022 03:58
Last Modified: 03 Aug 2022 23:58
Uncontrolled Keywords: helical structure of tetrahedra; boerdijk-coxeter helix; icosahedral aggregates of tetrahedra
Fields of Research (2008): 01 Mathematical Sciences > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4999 Other mathematical sciences > 499999 Other mathematical sciences not elsewhere classified
Identification Number or DOI: https://doi.org/10.3390/math7101001
URI: http://eprints.usq.edu.au/id/eprint/50532

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