Periodic Modification of the Boerdijk–Coxeter Helix (tetrahelix)

Garrett Sadler, Fang Fang, Richard Clawson and Klee Irwin
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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
Klee Irwin: Quantum Gravity Research, Topanga, CA 90290, USA

Mathematics, 2019, vol. 7, issue 10, 1-18

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”.

Keywords: helical structure of tetrahedra; boerdijk-coxeter helix; icosahedral aggregates of tetrahedra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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