On Three-Dimensional Space Groups

Details On Three-Dimensional Space Groups On Three-Dimensional Space Groups

1999-11-23

arxiv.org/abs/math/9911185v1

Mathematics

Metric Geometry

26 pages, 8 figures

Scientific paper

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.

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