  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".
