Symmetricks / Symétrucs & Tessellations

All this talk about sharing space between characters in a tessellation has made me think of the word “symétruc”, which I coined a few years ago in a discussion with Jeff Weeks, American mathematician and KaleidoPaint app programmer. My original intention was for a word better than the French “pavages”, or “dallages”, which to me aludes to floor tiles, patio stones or asphalt pavement, rather than graphic art. Tessellation can be used in French, I’ve since found out. Since then, I’ve used the word for this evolving technique of sharing space within a tessellation. A symmetry trick, or “symmetrick”, where one area of a tessellation is shared by more than one unit cell, or one full character. Jury is still not in court, to decide if this is legal or cheating. In my mind, it’s stretching the rules, exploring the possibilities, and letting intuition take over, once in a while.

Since the first blog post about symétrucs / symmetricks, I have used the technique in quite a few more tessellations. Below, I will show you fourteen of my more recent tessellations, involving symmetricks.


Biker tessellation Notice the 6-way sharing of the back wheel, and 3-way sharing of the front wheel. Not quite a true tessellation in my definition, as there is an incredible amount of negative (free, clear, empty) space, but still a cool symmetrick:

Cellphone Zombie 5, Prior to Impact    In this tessellation, the top half of the head is shared, sliced horizontally right through the eyeballs, a symmetrick I use often for symmetry groups containing blasted mirrors. Cool use of the 4-way rotation point to get the hashtag symbol:

Cellphone Zombie 4, Road Rash,  The road can be seen between his feet and off into the distance above his head. One of those yellow rectangles is drawn around the third rotation point, the 180 degree point. It allows the roadway to continue into the other character’s space. Guess the Zombie should do a 180 and check for the oncoming Mack truck:

Cellphone Zombie 2, PHD    These two guys are sharing the same phone around a 2-way rotation point. Completely oblivious to the world around them. Saw one of these in Qualicum a few weeks ago. Crossing at a four way stop, nose deep in his digital reality. I said to My friend loudly, “Hey, look, a cellphone Zombie”, the Zombie looked up and smiled. I was informed a few seconds later, that they would not all react in this friendly manner. PHD, by the way is short for “Push here dummy”:

You Talkin’ to Me?  In this tessellation, the horse/centaur/human/whatever is grabbing the tail of the other character next to him, and vise versa. Not really sharing the space but reaching into the space next door. A few of theses symmetricks too:

Down the Hatch   He is spilling wine into the other character’s mouth. Sharing or rather, spilling into the other character’s space.

Bald Eagle. Two instances of the eagle character are fighting for the same snake snack. Again, not really sharing the same space, but the story is spilling over next door and back again onto itself. Weird, I know:

Mouse Tessellation  sharing the same tail. Not funny and not nice said one friend having issues with rats in a rental unit:

Dog Walker,   In this tessellation I am allowing the leash to fly over to the neighbouring character to a dog testing the length of the restraint and patience of the dog walker.

Building a P4g character, A technical post, about the split head symmetrick, a very simple basic tessellation in symmetry group P4g. This post explains the tessellation process quite well, with step by step instructions for this specific symmetry group.

Follow Me, this Way  A side burn / thumb issue, dual purpose space, different interpretation to the area. Symmetrick sub group 3! Check the guy with the orange t-shirt, his left hand. It’s also the other guy’s hair and sideburn:

Follow me, this way! A tessellation by F.Champagne, ©2016,

American Football.  This is a difficult symmetry group as it is a box of four mirrors. Ugg. In this tessellation there is symmetrick sharing the top of the head and the football. One mirror to not forget is the one right down the middle of the player, the others are at the outside arm, the knees and ball and horizontally through the head:

Cuckoo’s Trattoria  For this tessellation, the chef is sharing the same hat and same pizza as the other chef. Wicked story this one. Go read it, especially if you come visit the Island:

The Artist, In this tessellation, the artists links arms together, the same way lovers link arms when sharing some wine. Paintbrush instead of wine glass. And they definitely look blasé, not in lust:

Totally enjoyable to come up with these cheats. Symmetricks/symétrucs. Push your limits. Doubt I will ever stop.



One thought on “Symmetricks / Symétrucs & Tessellations

  1. Pingback: Four Snails #Tessellation | Tessellations, images in regular division of the plane

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