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Manji, the Japanese Buddhist swastika symbol, forms a part of a typical Japanese p4gm pattern. Besides this ‘parent’ pattern, an interesting, affinely modified pgg variety and other derivatives are used. These form a subset of a family of swastika-meander patterns of classical Greek, Roman, Seldjuk, Ummayad and Buddhist art. In this vast body, families of ‘rotation homologues’ (p4 and p4gm, respectively), based either on ‘normal’ or ‘recurving’ swastikas or on their combination, as well as ‘inclusion derivatives’ which accommodate other elements besides swastikas, and other pattern types can be defined. A variety of swastika patterns was created by substituting the swastikas for squares, lozenges and triangles (as triskalions) of the Archimedean patterns. Plane groups with swastikas are altered into layer groups by assigning a ‘spin’ to each swastika. For example, p4gm alters into a layer group p4212. Kamon are heraldic symbols, originally used by aristocratic families, later also by commoners, guilds and temples. There can be one, three or five mon on a formal kimono. The medieval use of mon for friend-andfoe recognition in battles between clans is well known. The pictorial contents of kamon are rich: animals, plants, objects of everyday life and work, and pure geometric forms. Collections of kamon, such as that by Hondaso Ichiro (1992) show 2D point groups (from 16.m.m to 1) and layer groups, both of which show interesting variations derived skilfully from the symmetry of the object depicted, combinations of 2-3 different symmetries in one mon, as well as (projected) 3D groups and further motif varieties situated outside a point-group definition. As always in such cases, the statistics of the resulting symmetry groups is of great interest.

Microstructure and formation process of reddish color pattern hidasuki on bizen stoneware