Garrett Sadler, Fang Fang, Julio Kovacs, Klee Irwin (2013)

The Boerdijk-Coxeter helix is a helical structure of tetrahedra which possesses no non-trivial translational or rotational symmetries. In this paper we develop a procedure by which this structure is modiﬁed to obtain both translational and rotational (upon projection) symmetries along/about its central axis. The ﬁndings of several distinct periodic structures are reported and focus on two particular forms related to the pentagonal and icosahedral aggregates of tetrahedra, as well as Buckminster Fuller’s “jitterbug transformation”.