Symmetry Group Pmg

Are we ready for another creative brain gym session? These Pmg tessellations are built around two different glide reflections, one mirror, and two rotation points, at 180 degrees. (a.k.a., P2mg)

“Blue Rinse with Handbag” below, illustrates the mirror glide concept quite well. She sort of looks like plastic Fussball figures, and even rotates along that metal bar at about the right spot, at the height of the handbag clasp. You could flip her around easily. There is another glide right through the forehead. Must have drawn this while subconsciously remembering a soccer commentator throw an unusual image at his GOLTV audience. Something along the lines of players being confronted on the pitch by a bunch of old ladies with handbags. Out in left field these UK commentators. I guess you could call this symmetry group the Fussball figure group!

Symmetry Group Pmg-Blue-Rinse-with-Handbag-grid-on © 2013 Champagne Design

Symmetry Group Pmg-Blue-Rinse-with-Handbag-grid-on © 2013 Champagne Design

Easy to see the mirror as it constructs both sides of the Lady in blue. Red and green dots show the two different 180 degree rotation points.

Have a look at Big Foot below, and you will see the same pattern emerge. Try locating the two-fold rotation points, and the mirror. If you click on the images themselves, you’ll get a bigger view.

Symmetry Group Pmg-Big Foot - © 2013 Champagne Design

Symmetry Group Pmg-Big Foot – © 2013 Champagne Design

The tessellation is accomplished by drawing a line away from a rotation point to the mirror, for each of the rotation points, R1 and R2. The red line and green lines below show a quick outline of a possible standing figure once you tweak the final blue line for the legs. Much fun with this symmetry group.

Symmetry-Group-Pmg-explained

Symmetry-Group-Pmg-explained

The possibilities are endless. Bird Brainiac below is another example of Symmetry group Pmg.

Symmetry Group Pmg - Bird-Brainiac - © 2013 Champagne Design

Symmetry Group Pmg – Bird-Brainiac – © 2013 Champagne Design

There are 17 methods to divide the two dimensional surface into tessellations. This is post seven. Ten more symmetry groups to go!

Lots of software out there to help you accomplish this type of design.

An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks.

There is also a java-based program “Escher Web Sketch”  at the Ecole Polytechnique de Lausanne. Make sure Java is enabled and not blocked by your security software.

Also, another screen-based software by Anselm Levskaya Escher Sketch v2. (I used to have a basic Mac-based software, way back in prehistory, 1995, by the same name. It worked on the cutesy first Mac)

Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.

Comments are always welcome!

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