Symmetry in Combinatorial Structures

Dear Colleagues,

The Special Issue 'Symmetry in Combinatorial Structures' should be related to geometric objects, for which their abstract properties are given with combinatorial automorphisms, and their existence (perhaps with geometric symmetries) has to be decided. Here are some examples of possible topics.

Regular maps (a source of symmetry groups and a natural generalization of Platonic solids) and their questionable topological or polyhedral embeddings in 3-space.

Symmetric abstract point-line configurations in the sense of Branco Grünbaum and their embeddings.

Possible additional candidates of regular maps for regular Leonardo polyhedra.

Non-convex 2-spheres with properties like Archimedean bodies similar to the union of the 15 truncated cubes depicted above (refer to the graphical abstract).

Please click on the following video link for more details: https://youtu.be/AailDBdIPVY.

We invite contributions (original research and review articles) covering a broad range of topics around combinatorial and geometric symmetries.

Prof. Dr. Jürgen Bokowski
Prof. Dr. Isabel Hubard
Guest Editors

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• combinatorial and geometrical automorphisms of surfaces, sphere systems and manifolds
• graph theory
• embeddings
• surfaces and manifolds
• discrete geometry
• symmetry groups
• geometric polyhedra
• regular maps