Other possible symmetry point, two patterns symmetric one to the other with respect to their common vertex form together a new repetitive surface, the center of which is not necessarily symmetry point of its content.Ĭertain rotational symmetries are possible only for certain shapes of pattern. Other example, the midpoint of a full side shared by two patterns is the center of a new repetitive parallelogram formed by the two together, center which is not necessarily symmetry point of the content of this double parallelogram. For example its diagonals intersect at their common midpoints, center and symmetry point of any parallelogram, not necessarily symmetry point of its content. Groups are registered in the catalog by examining properties of a parallelogram, edge‑to‑edge with its replicas. It may be added that a well‑known theorem deals with colors. Certainly a color is perceived subjectively whereas a wallpaper is an ideal object, however any color can be seen as a label that characterizes certain surfaces, we might think of a hexadecimal code of color as a label specific to certain zones. represents the same wallpaper on the following image 4, by disregarding the colors. For example image 1 shows two models of repetitive squares in two different positions, which have equal areas of a. Such pseudo‑tilings connected to a given wallpaper are in infinite number. Such repeated boundaries delineate a repetitive surface added here in dashed lines. Conversely, from every wallpaper we can construct such a tiling by identical tiles edge‑to‑edge, which bear each identical ornaments, the identical outlines of these tiles being not necessarily visible on the original wallpaper. More particularly, we can consider as a wallpaper a tiling by identical tiles edge‑to‑edge, necessarily periodic, and conceive from it a wallpaper by decorating in the same manner every tiling element, and eventually erase partly or entirely the boundaries between these tiles. Any periodic tiling can be seen as a wallpaper.
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