Group Pmm is also known as P2mm in Peter S. Stevens’ Handbook of Regular Patterns. A four-sided mirrored box. Figures with bilateral symmetry work best in this type of group.

One for each mirror is a possibility. A line drawn from each mirror corner to its twin will delineate the four figures into a tessellation.

The image below shows a Pmm symmetry group tessellation, fully zoomed-out. The rectangular structure is quite apparent. Of course, the trick is to turn all of this into a recognizable object!

Group-pmm – Rockie and the Three Dudes (zoomed-out) – © 2013 Champagne Design

This is the same tessellation, zoomed-in. It shows the unit cell, the rectangle, with its four mirrors.

Symmetry Group Pmm – Rockie and the Three Dudes – © 2013 Champagne Design

Mosquito / Moth / Beaver / Boy is another example of this Pmm symmetry group.

Symmetry Group Pmm – Mosquito-Moth-Beaver-Boy – © Champagne Design 2013

Have fun with the KaleidoPaint iPad app. I will attempt to illustrate all 17 ways you can divide a two dimensional surface with this cool app, from the billions of possible drawings.

If you don’t have an iPad, you can try the Java-based program “Escher Web Sketch” at the Ecole Polytechnique de Lausanne. It works just as well to create your shapes.

Or this screen-based software by Anselm Levskaya Escher Sketch v2.

Comments are always welcome!