The Complete Rubber Ducky Collection: a series of tessellations, eighteen of them, covering the complete range of classic tessellation symmetry groups, plus Elvis! All of these rubber ducky tessellations, all eighteen, were crafted and refined, in the space of fourteen days, from May 24, 2021, to the sixth of June. Quite a feat for me. When creativity is in the air sprinkled with intuition, follow the flow and take advantage of it, good things can happen. Where does this topic originate you ask? I have a rubber ducky on the handlebar of my bike. It squeaks and has flashy disco lights.

In no particular order, but first created for the series, is “CANARD À L’ORANGE”. A single bulbous character, slightly orange in colour, repeated using symmetry group Pmg, what I like to call my “foosball” symmetry system, where the repeated ducks are flipped around a central horizontal bar, just like in the foosball game.

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The second tessellation using the Rubber Ducky theme, is “RUBBER DUCK IN RUBBER BOOTS”. One classic ducky floating on by, and the other one at cross angles, wearing wellies. Somehow, when you tilt your head, it seems like the floating-on-by duck’s bill is part of this other character, as its ears. The real symmetry classification, for you nerds, is Cm.

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“DUAL DUPLE DUCKS” is the third in this collection. Both of them share space with another instance of themselves. The really saturated yellow duck shares its bottom bill with itself. The pale yellow duck shares its eyeballs with another reflected instance of itself. The reflected beak sort of looks like red hair. This tessellation is built in symmetry group Cmm, what I like to call Kaleidoscope 3. It is built inside a 30/60/90 degree triangle.

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My fourth attempt was using symmetry group P6, a 6-way, a 3-way and a 2-way rotation, in a circuit around a hexagon. I call this symmetry group my favourite half-dozen. This ducky tessellation is called “FLOWER BILL DUCKY”. An unusual white outline, for me anyhow, a lumpy ducky, six of them with beaks all wedged-in together, pinkish in colour, so much so that it looks like they are hiding behind a flower.

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“BRAIN BUCKET DUCK”, a slow whiz-by and a gander at the one/many ducks in the race. One watching, one participating. Two ducks in this P1 symmetry group, a simple Up/Down, Left/Right translation (repetition) of the characters in a group. This is number five in the series, I was wondering how far I could get with this topic. Seems to the end.

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The sixth one in the collection is challenging me for a title. “DUCK IN DISGUISE”, it is for now. Trying to look human with his undershirt. Might be sensitive to the sun, got too close to some Giant Hogweed. The tessellation was built using symmetry group P2, which uses a parallelogram with alternating two-way rotation points.

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Versatile creatures, underwater forays, swimmers, waddling land strolls and flight. Well, the non rubber ducky one that is. And versatile shapes, rounds and peaks, curves and wedges, all molding themselves into perfectly nested shapes. “DRAKE AND DAUGHTER” is the title here, a tessellation in symmetry group P3, three different three-way rotation points.

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From the old French fairy tales, I’ve name this one “RIQUET À LA HOUPPE”, Riquet of the Tuft, being an unusual hairstyle. Symmetry group P4, a fairly complex mesh of four identical two-way rotations, and two different two-way rotations. The four-way twirl of the tuft is obvious, and somewhat too is the slight curl in the tail. The other two-way rotation, not as visible, located on the far side of his breast, above the far wing.

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What the heck is a “BLUE FOOTED BOOBIE”, another rubber ducky tessellation with a salute to that unusual creature. A tessellation of two rubber duckies, the Blue Footed Boobie, and an astonished spectator to his dance. This one uses symmetry group Pm, alternating parallel mirrors, creating stacks of characters. It’s worth a google to see him dance and prance.

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The tenth tessellation in this series, “SQUEAKING DUCK”, is seen from above, as if densely packed floating down the canal, in a popular rubber ducky race. Might be nice to fly a drone above the duck race, it might look like this tessellation. This drawing is built using an equilateral triangle, of three identical mirrors, with a three-way rotation point in the middle, symmetry group P31m, the mirrored triplets I like to call this method.

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This tessellation might be part of two collections, “CELLPHONE ZOMBIE DUCKIES”, I already have an extensive collection of cellphone zombie tessellations. These nested shapes are built following a similar system as above, an equilateral triangle but with three different mirrors and no rotation in the middle, group P3m1, I like to call ménage à trois, or kaleidoscope 1. Enjoy their obsessions.

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The “GRAND DOOKY OF ERRINGTON”, a play on words of the Grand Duchy of… a whole list shows up on Google. An older drake going about his stroll, built in symmetry group Pgg, a this-way, that-way kind of system. An alternating sequence of two-way rotation points, at his belly and behind the wings.

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Oh, oh, this is number 13, called “UNSINKABLE RUBBER DUCKIES”, a pair of safety conscious duckies, leaving nothing to chance when heading out on the water. Two parallel glide reflections are the system behind this tessellation, symmetry group Pg. One’s wearing a PFD, the other a flimsy lifebuoy. Good luck ducks. Have fun!

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P4g is the symmetry here, a four-way rotation inside a mirrored square. “PEPPY DUCKY” is the name here. A four-way rotation, easy to spot those wing tips, and four identical mirrors. One of my cheats, the sharing of space between instances of the character, if you look closely, there is a mirror in the middle of his body, a vertical one, but also a horizontal one, smack in the middle of his eyeballs. The reflected beak could work as a ball cap. Weirdly enjoyable.

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“PROPELLER PALS”, four rubber duckies in symmetry group Pmm, a box made of four different mirrors but without any rotation point in the middle. A few sleepy duckies, and the other two a bit more excited about life, the universe and everything.

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I’m starting to understand this P6m symmetry group a bit more lately. Six mirrors crossing at a six-way rotation point creates 12 triangles where you need to place your whole topic. My previous success was the Browder Safety Net. This one is not as busy, only three different ducks. And the central lily pad. I’ve titled this “POPULOUS POND WITH PADS”.

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And the last tessellation, true nested shape with this rubber ducky topic, “AAAANATIDAE”, the scientific name for ducks, plus the preceding three A for Angry, Astonished and Asleep. Another triangular symmetry group of mirrors, P4m, 45/45/90 degrees. This whole scene, seen from above. Created all within a tiny sliver of a wedge, repeated 12 times around the lilypad.

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And an extra bonus tessellation for an enthusiastic fan of my work, Elvis Duckley. Completed this morning. Symmetry group Cm, alternating parallel mirror and glide.

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I hope you have enjoyed this longish diatribe about rubber duckies and tessellations. May it spur you to try your hand at drawing these interesting nested shapes. In the next months, I will continue uploading classes to Skillshare, a teaching platform for creative individuals. The first class is on symmetry group P4g, the four-way rotation inside a mirrored box. The tessellation called Peppy Ducky, above, was constructed using this method. Send me an email if you want two weeks free access to all the classes.

Cheers!

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