research papers

An attempt has been made to deduce the condition necessary for diffraction enhancement of symmetry to occur in the diffraction pattern of a structure

**X**, and because the symmetry of the diffraction pattern of**X**coincides with that of its vector set**V**, the symmetric feature of**X**derived from the symmetry of**V**was studied. The symmetry with the point group**G**or_{V}**G**/_{V}**G**according as_{I}**X**is inversion-symmetric or not, is defined as the vector symmetry of**X**, where**G**is the point group of_{V}**V**and**G**, is the inversion group, and when the vector symmetry of_{I}**X**is**C**_{n}, for example,**X**is specified as**C**_{n}-vector-symmetric. When**X**is homometric with itself by a rotation of 2*π*/*n*, it is specified as*n*-fold self-homometric.**X**being*n*-fold self-homometric is the necessary and sufficient condition for**X**to be*n*-fold vector-symmetric. Also,**X**exhibits an enhanced vector (diffraction) symmetry if it is a space-groupoid structure with the kernel whose point-group symmetry is, other than by addition of an inversion, higher than the point-group symmetry of**X**. Four examples of enhanced vector symmetry are examined.