GeoCombSurfX - Exploring Properties of Polygonal Complexes

Explore the fascinating world of polygonal complexes in this JuliaCon 2024 conference talk by Sascha Stüttgen and Reymond Akpanya. Delve into the basic definitions and underlying theory of convex and non-convex polyhedra and their corresponding polygonal complexes. Discover how to analyze these structures from both combinatoric and geometric perspectives, including isomorphism groups, vertex and edge colorings, and embedding challenges. Learn how Julia's diverse package ecosystem and performance make it an ideal platform for developing software to study polygonal complexes. Examine the interlocking problem of 3D block assemblies as a practical application, and understand how Julia packages like Polyhedron.jl, JuMP.jl, and HiGHS.jl can be utilized to tackle this challenge. Gain insights into future developments of the GeoCombSurfX package, including integration with the OSCAR project for algebraic analysis and plans to parameterize embeddings of polygonal complexes with triangular faces into 3D space.