Catalog of friezes
A frieze is a motif that repeats along a strip, that is, a region of the plane bounded by two parallel lines. Such motifs appear frequently in architecture and art, especially in decorations, tiles and wallpaper. In the mathematical classification, each frieze corresponds to a group of plane isometries. Below are all 7 possible friezes, named with the crystallographic notation and, in brackets, with the orbifold notation. For each frieze, one possible method (not the only one) to reproduce it is shown [1].
p1(∞∞)
Shape to select:
rectangle, square or rhombus.
Internal configuration of the tile:
free, with no internal symmetry.
Frieze:
the tile repeats itself by translation.
p11g(∞×)
Shape to select:
triangle.
Internal configuration of the tile:
free, with no internal symmetry.
Frieze:
a glide reflection is applied to the tile, with its axis parallel to the frieze.
p11m(∞*)
Shape to select:
rectangle or square.
Internal configuration of the tile:
symmetry about the midline of the frieze.
Frieze:
the tile repeats itself by translation.
p1m1(*∞∞)
Shape to select:
rectangle or square.
Internal configuration of the tile:
free, with no internal symmetry.
Frieze:
the tile repeats by an axial symmetry with its axis perpendicular to the frieze.
p2(22∞)
Shape to select:
rectangle, square or rhombus.
Internal configuration of the tile:
central symmetry.
Frieze:
the tile repeats itself by translation.
p2mg(2*∞)
Shape to select:
triangle.
Internal configuration of the tile:
symmetry about an axis perpendicular to the frieze.
Frieze:
the tile repeats by central symmetry.
p2mm(*22∞)
Shape to select:
rectangle or square.
Internal configuration of the tile:
symmetry about the midline of the frieze.
Frieze:
the tile repeats by an axial symmetry with its axis perpendicular to the frieze.
