HHHHHHHHH have glide reflections from one cell to the next but not within the cell.] Also when you look for glide reflections they must be within the cell which means that the translation length of the glide reflection must be one half of the translation length mapping one cell to the next. For example in the pattern E E E E E EĮ E E the enlargement does not map the whole strip into itself and this is counted as the same frieze type as FFFFFFFFF. [Some words of warning: There may be other symmetries within the cell (such as quarter turns or enlargements) but these symmetries should not be taken into account because they do not transform the whole strip into itself. Frieze patterns are classified according to whether each of the four symmetries do or do not occur, and you can use a decision tree to do this classification. In the letter S) and G for a glide reflection (as in bp). We shall call the four symmetries H, V, R and G: that is H for reflection in a mirror line along the strip (horizontal reflection, a symmetry which occurs in the letter D) V for reflection in a mirror line perpendicular to the strip (vertical reflection, as in A) R for rotation by a half turn (as This article first gives a simple way of sorting friezes into the seven types and then explains why there are only seven.Īpart from translation, there are four other symmetries which transform the strip into itself. Perhaps surprisingly mathematicians say that there are only seven different frieze patterns. Piece of the pattern to be repeated by translations. This defines the 'cell' which is the smallest In distinguishing one frieze pattern from another we first need to find the smallest translation length in the strip. All frieze patterns have a section of the pattern which is repeated alongside itself (we call this a translation). Repeating strip patterns, called friezes, occur all over the world in border decoration in buildings, textiles etc.
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