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Periodic modification of the Boerdijk-Coxeter helix (tetrahelix)

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arxiv 1302.1174 v1 pith:BNJROYCJ submitted 2013-02-02 math.MG cond-mat.mtrl-sci

Garrett Sadler , Fang Fang , Julio Kovacs , Klee Irwin This is my paper · ORCID
classification math.MGcond-mat.mtrl-sci
keywords boerdijk-coxeterhelixperiodicrotationalstructuresymmetriestetrahedratranslational
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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 report the finding of several, distinct periodic structures, and focus on two particular forms related to the pentagonal and icosahedral aggregates of tetrahedra as well as Buckminster Fuller's "jitterbug transformation".

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