For example on image 2, a Pythagorean tiling is sometimes called pinwheel tilings because of its rotational symmetry of 90 degrees about the center of a tile, either small or large, or about the center of any replica of tile, of course. 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. On the next page, we'll see tiles that DO flip over.Any periodic tiling can be seen as a wallpaper. The cats and the ducks are also "tiles" that translate/slide/glide left or right, up or down, to fill in the picture. Now take a look at the other pictures on this page. The original line XY is "translated" along the Y axis to make line X 1Y 1. In math class, we'd say that we can move a line along a graph by saying "X=Y" for the original line and "X 1 + 4 = Y 1" for the line that would be 4 boxes above it on a piece of graph paper. So, why do we call it "translation"? Well, we call that movement a "translation" because we "translate" the tile along the X-axis and the Y-axis. This kind of tessellation symmetry- tile repeating- is called Translation and/or Sliding. The tiles in this picture are copies of one another that are simply shifted from one place to another, without tilting or flipping them over or resizing them. The tessellation is made by repeating the tile over and over again, and fitting all the copies of the tile together. This is the basic "tile" shape of the first tessellation on this page. How to Make an Asian Chop (stone stamp).
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