Glide Reflection and other Combined Transformations

Rinus Roelofs
Bridges: Mathematical Connections in Art, Music, and Science (2004)
Pages 141–148


Glide Reflection is one of the four (translation, rotation, reflection and glide reflection) symmetrie transformations we use to classify the regular divisions of the plane. In a way glide reflection is somewhat different from the other three, because it's not a simple transformation. In fact it is a combination of two transformations: translation and reflection. A combination of two but used as a single combined transformation. This article is about my work with other combinations of transformations that could be used as a combined transformation and how these transformations could be used in the design of patterns and objects. I define three other transformation which will be explained in the article. The transformations are not restricted to the 2D plane, but are used in the 3D space. Most of the examples are 3D objects or designs.