Gelbe Karte in Pmm – a difficult symmetry group

Took a while, but I finally came up with a tessellation I like, to represent this Pmm symmetry group. I’ve named it “Gelbe Karte”, yellow card. This tessellation is built with five characters, Höwedes, Asamoah, Kolasinak, the Ref, and the one receiving a yellow card for excessive simulation (diving), Robben. About time Arjen gets a card.

Gelbe Karte tessellation by Francine Champagne ©2016

Gelbe Karte tessellation by Francine Champagne ©2016

This Pmm symmetry group is a challenge; MC Escher only did one tessellation following these rules. MCE created the “4 motifs system” which I have an example in another post, the Bird/Butterfly/Bat/Fly. I don’t find mirrors graphically interesting, and prefer other symmetry groups with glides, rotations and translations. If the mirror is in combination with another symmetry operation, then it’s not too gross! Below is an example using Pmm and my mimed hands, a modifiable box of four mirrors, it can be skewed to any proportion but that would still not save it as a system.

Symmetry Group Pmm, a modifiable box of four mirrors, it can be skewed to any proportion

Symmetry Group Pmm, a modifiable box of four mirrors

Having been challenged to create something in this symmetry group, I have since come to understand some of its versatility. It can be used to tessellate one figure, four figures, five figures or even more. My original attempt, quite a few years ago was built with one figure, I called it “Fred Waving”; this was in the old days when KaleidoPaint did not have its superb “edit line” function. You can see how messy the drawing is, colours painted over lines I didn’t like, with different curves redrawn on top. Still, it does not fulfill the definition of a true tessellation, where there are no empty spaces between the characters. This one was wallpaper to me, not a tessellation.

Fred Waving tessellation by Francine Champagne ©2013

Fred Waving tessellation by Francine Champagne ©2013

The same goes for the “Butterfly Hands” below, too much space all around for it to be a true tessellation, true nested shape. This is the tessellation that gave me the idea for using hands to explain symmetry groups in a post a few weeks ago: Symmetry group thumbnails and listing systems

Butterfly Hands tessellation by Francine Champagne ©2013

Butterfly Hands tessellation by Francine Champagne ©2013

American Football is a tessellation using one figure. But not a true one to me unless I gave him really square shoulders and pointy elbows. I used my mirror cheat twice here, one football for two guys and one head for two guys. No comment intended. Other mirrors are right down the middle of the character and on the length of his arm. Ug.

American Football tessellation by Francine Champagne ©2016

American Football tessellation by Francine Champagne ©2016

Here he is again, a little less nerdy. Knees bent on the ground have been added, making it a little more believable. A solid wall of offensive players, each with their own ball. I could alternate the jersey colours and that would illustrate the two different teams.

American Football 2 tessellation by Francine Champagne ©2016

American Football 2 tessellation by Francine Champagne ©2016 (everybody is on the same team and plays the same position!)

I did attempt at placing four different characters each on their own mirror. Quite a few sketches done before being able to complete one. Sigh. All so constricted and rigid, on top of being my usual comic book style. Still working on a few more.

 

One thought on “Gelbe Karte in Pmm – a difficult symmetry group

  1. Pingback: Sharing the walls with M.C.Escher in Italy | Tessellations, images in regular division of the plane

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