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

We show that for every convex polyhedral sphere $P$ in $S^3$, there exist twocanonical, non-edge-to-edge tilings of $S^{2}$ whose tiles are given by all thefaces of $P$ and the dual convex polyhedral sphere $P^*$ to $P$. Under theidentifications of $S^{3}$ with the Lie group $SU(2)$, and of $S^{2}$ with theunit sphere in the Lie algebra $su(2)$ of $SU(2)$, our result is obtained byconsidering the set $\widetilde P$ of outward unit normal vectors to $P$ andthe maps from $\widetilde P$ to $S^{2}$ defined by using the left and rightMaurer-Cartan forms on $SU(2)$.

Convex Polyhedra in the $3$-Sphere and Tilings of the $2$-Sphere