Report of a Subcommittee on the Nomenclature ofn-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space groupsSubcommittee renewed by the IUCr Commission on Crystallographic Nomenclature 18 March 1999 with all present co-authors as members. Original version of the Report received by the Commission 22 April 2002, accepted 19 July 2002.

Abstract

The Second Report of the Subcommittee on the Nomenclature of n‐Dimensional Crystallography recommends specific symbols for R‐irreducible groups in 4 and higher dimensions (nD), for centrings, for Bravais classes, for arithmetic crystal classes and for space groups (space‐group types). The relation with higher‐dimensional crystallographic groups used for the description of aperiodic crystals is briefly discussed. The Introduction discusses the general definitions used in the Report.

Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. I. Crystal families in five-dimensional space with two-, three-, four- and sixfold symmetries

“…In a subsequent paper , the Weigel-Phan-Veysseyre (WPV) symbols (Weigel et al, 1987) of 15 families, from family I to family XV, were given together with a detailed study of a specific family, No. This study complements the results given in two reports of the IUCr Subcommittee on Nomenclature of n-Dimensional Crystallography (Janssen et al, 1999(Janssen et al, , 2002. In the present paper we assign symbols to the point groups of the following crystal families: the (monoclinic di squares)-al family (No.…”

“…We recall that, by convention, the crystal-family numbers are Roman numbers (Weigel & Veysseyre, 1993;Plesken, 1981;Plesken & Hanrath, 1984) or Arabic numbers (Janssen et al, 1999(Janssen et al, , 2002Brown et al, 1978) for crystal families of space E 4 , and Roman and Arabic numbers (Janssen et al, 1999) for crystal families of space E 5 .…”

Software package for structure analysis of quasicrystals∗

“…(For the generators see [4].) For the symbols of n D space groups, we have no standard ones, but IUCr has proposed their recommended symbols, although these symbols are not widely used yet [12]. For example, the diffraction patterns of the b-Ni phase in decagonal Al-Ni-Co quasicrystals show systematic extinction rules, which is consistent with the space group P10 5 /mmc(5 2 1 mm).…”

“…In the case of b-Ni, they are at ±( j, j, j, j, 5z)/5 ( j = 1, 2; z = 1/4) as mentioned in section 2. Their site symmetry group is 5/mm2(5 2 1m1) [12]. In polygonal quasicrystals, the OD is an object in the 2D internal space.…”

Personal reflections on the history of aperiodic crystals from early days to the state of the art

“…A full list of all these groups can be found in his home page on the WEB (www.nims.go.jp/aperiodic/ yamamoto/index.html). The new conventions have been formulated by the nomenclature commission of the IUCr [15,16]. The diffraction patterns of quasicrystals show a new type of crystallographic symmetry: scaling invariance.…”