Groupoids: A Crystallographic Topology Perspective Carroll K. Johnson Chemical and Analytical Sciences Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37831-6197, USA The symmetry of finite objects is often difficult to describe algebraically without ignoring boundary and truncation effects. The 230 infinite crystallographic space groups provide suitable approximation for macroscopic crystals, but are inadequate for crystals containing only a few unit cells. Space group theory also fails to describe a truncated symmetry set such as that of an asymmetric unit (fundamental domain) within a space group. One approach for the asymmetric unit is to topologically wrap it up into a closed quotient space Euclidean 3-orbifold. A second approach involves groupoids which provide algebraic machinery for handling each of the above incomplete group problems. The first task is to incorporate groupoids into a crystallographic orbifold nomenclature system using the screw and glide groupoids introduced by M. A. Jaswon and M. A. Rose in "Crystal Symmetry: Theory of Colour Crystallography", Horwood, 1983. Screw and glide groupoids nomenclature is closely related to that in the Hermann-Mauguin space group notation, thus providing a possible method for describing orbifolds in a notation familiar to crystallographers. A second task is to translate our Gaussian measure based Radon Nikodym model for Morse functions on orbifolds, which we use to describe crystal structure topology, into the terminology of measured groupoids.