  In this paper we present the construction of several aggregates of
tetrahedra. Each construction is obtained by performing rotations on an initial
set of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or
(2) exhibits an aperiodic nature. Following this rotation, gaps of the former
case are "closed" (in the sense that faces of adjacent tetrahedra are brought
into contact to form a "face junction") while translational and rotational
symmetries are obtained in the latter case. In all cases, an angular
displacement of {\beta} = arccos((3{\phi} - 1)/4) (or a closely related angle),
where {\phi} is the golden ratio, is observed between faces of a junction.
Additionally, the overall number of plane classes, defined as the number of
distinct facial orientations in the collection of tetrahedra, is reduced
following the transformation. Finally, we present several "curiosities"
involving the structures discussed here with the goal of inspiring the reader's
interest in constructions of this nature and their attending, interesting
properties.
