English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we present the construction of several aggregates oftetrahedra. Each construction is obtained by performing rotations on an initialset of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or(2) exhibits an aperiodic nature. Following this rotation, gaps of the formercase are "closed" (in the sense that faces of adjacent tetrahedra are broughtinto contact to form a "face junction") while translational and rotationalsymmetries are obtained in the latter case. In all cases, an angulardisplacement 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 ofdistinct facial orientations in the collection of tetrahedra, is reducedfollowing the transformation. Finally, we present several "curiosities"involving the structures discussed here with the goal of inspiring the reader'sinterest in constructions of this nature and their attending, interestingproperties.

Cabinet of curiosities: the interesting geometry of the angle {\beta} = arccos((3{\phi} - 1)/4)