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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Cubic polyhedra with icosahedral symmetry where all faces are pentagons orhexagons have been studied in chemistry and biology as well as mathematics. Inchemistry one of these is buckminsterfullerene, a pure carbon cage with maximalsymmetry, whereas in biology they describe the structure of spherical viruses.Parameterized operations to construct all such polyhedra were first describedby Goldberg in 1937 in a mathematical context and later by Caspar and Klug --not knowing about Goldberg's work -- in 1962 in a biological context. In themeantime Buckminster Fuller also used subdivided icosahedral structures for theconstruction of his geodesic domes. In 1971 Coxeter published a survey articlethat refers to these constructions. Subsequently, the literature often refersto the Goldberg-Coxeter construction. This construction is actually that ofCaspar and Klug. Moreover, there are essential differences between this(Caspar/Klug/Coxeter) approach and the approaches of Fuller and of Goldberg. Wewill sketch the different approaches and generalize Goldberg's approach to asystematic one encompassing all local symmetry-preserving operations onpolyhedra.

Goldberg, Fuller, Caspar, Klug and Coxeter and a general approach to local symmetry-preserving operations