The types of transformations that are used in the generation of Frieze tiles include translations, glides, reflections, and rotations. Translations are incorporated with the concept of a 'net'. A net is a set of nodes which are separated by instantiation of a pair of translations u,v. The five basic net types use in Frieze tiles are rectangular, square, parallelogram, hexagonal and centered. Rectangular nodes require only that the two tranlations produce vectors that are perpedicular to one another.
Square nodes are a special case of rectangular that require that the length of the vectors be equal.
Parallelogram, is the general case and can be used for almost all techniques except when 3 or 6 fold rotations are required. Hexagonal nodes are composed of two vectors that are 60 degrees apart and of equal distance. The final net is a special case of rectangular which includes the central point of the rectangle as a node. Once a net type has been chosen, then one or more affine transformations are chosen to couple with the net node to produce a unique pattern. The affine transformations include, reflections, glides, and rotations.