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Regular polygonal complexes in space, I

Regular polygonal complexes in space, I

A polygonal complex in Euclidean $3$-space $\mathbb {E}^3$ is a discrete poly- hedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number $r\geqslant 2$ of faces surround each edge. It is said to be regular if its symmetry group is transitive …