1999/11/23 by John H. Conway, John Conway, Conway, John +6
Chemistry · Materials Science · Mathematics · #20H15 #51F15 #Crystallography and molecular interactions #Enzyme Structure and Function #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metric Geometry (math.MG) #math.GT #math.MG #msc:20H15 #msc:51F15
paper · pdf · doi:10.48550/arxiv.math/9911185
26 pages, 8 figures
arxiv created 1999/11/23 · openalex publication_date 1999/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.