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

Frucht showed that, for any finite group $G$, there exists a cubic graph suchthat its automorphism group is isomorphic to $G$. For groups generated by twoelements we simplify his construction to a graph with fewer nodes. In thegeneral case, we address an oversight in Frucht's construction. We prove theexistence of cycle double covers of the resulting graphs, leading to simplicialsurfaces with given automorphism group. For almost all finite non-abeliansimple groups we give alternative constructions based on graphic regularrepresentations. In the general cases $C_n,D_n,A_5$ for $n\geq 4$, we providealternative constructions of simplicial spheres. Furthermore, we embed thesesurfaces into the Euclidean 3-Space with equilateral triangles such that theautomorphism group of the surface and the symmetry group of the correspondingpolyhedron in $\mathrm{O}(3)$ are isomorphic.

Surfaces with given Automorphism Group