Regular Polygonal Complexes in Space, Ii

Regular polygonal complexes in euclidean 3-space E3 are discrete polyhedra-like structures with finite or infinite polygons as faces and with finite graphs as vertex-figures, such that their symmetry groups are transitive on the flags. The present paper and its predecessor describe a complete classification of regular polygonal complexes in E3. In Part I we established basic structural results for the symmetry groups, discussed operations on their generators, characterized the complexes with face mirrors as the 2-skeletons of the regular 4-apeirotopes in E3, and fully enumerated the simply flag-transitive complexes with mirror vector (1, 2). In this paper, we complete the enumeration of all regular polygonal complexes in E3 and in particular describe the simply flagtransitive complexes for the remaining mirror vectors. It is found that, up to similarity, there are precisely 25 regular polygonal complexes which are not regular polyhedra, namely 21 simply flag-transitive complexes and 4 complexes which are 2-skeletons of regular 4-apeirotopes in E3.