61 models
This is a 3D model of the world's first "einstein", an aperiodic monotile. Update: There's a chiral (handed) aperiodic monotile now, see: https://www.printables.com/model/494205-spectre-worlds-first-chrial-aperiodic-monotile You will…
This is a 3D model of the world's first chiral aperiodic monotile. “Chiral” means “handed” -- same as left and right handed screws you can't transform left into right just by turning the object. It's an update to…
Aperiodic tile cookie cutter based on the Smith, Myers, Kaplan, and Goodman-Strauss's aperiodic monotile. For information on this tile see https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/ . The cutter was used on ginder bread…
Aperiodic tiling, folks, is like the 'Jazz' of geometry. It's got some rules but loves to improvise! Picture a floor covered in tiles, but not the kind that make you think, "Oh, I've seen that pattern a million times." No, these tiles are…
For many years, mathematicians have been intrigued by the concept of aperiodic tiling - the idea that shapes can be arranged in such a way as to create infinite patterns that never repeat. However, until recently, it remained unclear…
An aperiodic monotile, sometimes called an "einstein", is a shape that tiles the plane, but never periodically. For more information about this shape, see: website dedicated to this shape video showing the space of related shapes paper…
These are two cookie cutters based on the aperiodic monotile ("one stone") shapes discovered by David Smith as described here: https://www.nytimes.com/2023/03/28/science/mathematics-tiling-einstein.html Flip some of your cookies for the…
This is a decorated version of the Hat aperiodic monotile. It includes three “pipes” joining the √3 sides of that tile. The result is quite mesmerizing, with an aesthetic reminiscent of the Tantrix/Palago-style puzzles and the Celtic…
This is a cheap and easy way to experiment with the new family of aperiodic monotiles discovered by: David Smith , Joseph Samuel Myers , Craig S. Kaplan and Chaim Goodman-Strauss . You can find more info here:…
This is maths, it's a tile, and now it's a toy :) You can tile the plane with it. With no gaps. Any way you tile it, you can never find a repeating pattern that continues paving the plane. About 50 years after the Penrose tiling's…
A parametrized version of the newly discovered Spectre, an Aperiodic Chiral Monotile. See: https://cs.uwaterloo.ca/~csk/spectre/ for more details about this shape. This version includes the OpenScad file, so you can modify the “polygon…
This model is a “from the ground up” recreation of the Einstein aperiodic tessellation. I built this using a series of construction lines to form a set of “allowed vertices” and then “walked” from point-to-point by specifying the angle…
Loudspeaker enclosure with aperiodic (resistive) vent to avoid harmful resonance of insufficient air volume. Inner surface consists of two types of quadric surfaces (parabola and ellipse) that share common locus. Aperiodic vent can be…
This is a Spectre. It is an aperiodic monotile, or "Einstein": A shape that tiles the plane, but only nonperiodically. More specifically, it tiles the plane nonperiodically without using a mix of normal and mirror image shapes . Spectres…
I'm surprised nobody's done anything like this yet. It's a nice pattern. The base vector was pilfered from https://cs.uwaterloo.ca/~csk/hat/app.html if you want to have fun with it yourself. I've also included the uncropped inner…
In March 2023 finally the first “Einstein” was discovered! As a big fan of the Penrose Tiles, especially P2 (kites and darts), i read an article on derStandard (german) today and i just needed to make this happen. In this article i found…
This is the turtle variation of the aperiodic monotiles found by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss announced in March 2023 . An aperiodic monotile, sometimes called an “einstein,” is a shape that…
A set of recursive OpenScad scripts to generate some aperiodic tilings of the plane: Ammann-Beenker , Armchair , Chair , Domino , Golden Triangle , Half-Hex , House , Penrose , Pentomino , Pinwheel , and TriHex . The STL and GCODE files…
As described in Smith, D., Myers, J. S., Kaplan, C. S., & Goodman-Strauss, C. (2023). An aperiodic monotile. arXiv preprint arXiv:2303.10798 . Unlike some other models that are derived from Craig Kaplan's interactive tiling toy , the…
This is a little different than other monotile uploads here. I've taken the extra step to produce multiple aspect ratios for the right-angle edges. So you can have a different monotile set than everybody else ;) My favorite is the Phi…
A cookie or clay cutter in the shape of the aperiodic monotile einstein shape, published by Smith and friends in March 2023. Smith, D., Myers, J. S., Kaplan, C. S., & Goodman-Strauss, C. (2023). An aperiodic monotile. arXiv preprint…
Smith, Myers, Kaplan, and Goodman-Strauss's aperiodic monotile, the Hat, smooth on one side and with Dan Piker's Truchet-like markings on the other side in relief. As discovered in March 2023, this single shape tiles the plane but only…
On March 20, 2023, a group of computer scientists (David Smith, Joseph Samuel Myers, Craig Kaplan and Chaim Goodman-Strauss) revealed their discovery of the holy grail of tiles. A simple 13-sided shape, nicknamed the "hat polykite", is…
This is a follow up by David Smith , Joseph Samuel Myers , Craig S. Kaplan , Chaim Goodman-Strauss of their discovery of an aperiodic monotile two months ago. Yesterday (may 29, 2023) they announced they now have found a family of tiles…
Update: Added options for marking top and/or bottom of tiles with Truchet-tile like arcs. A jigsaw puzzle made of these mono tiles could be really insane. Turn filament scraps into colorful tiles to make interesting designs! This tile is…
A 3D model for 3D printing the aperiodic monotiles, described in the paper by Smith et. al. Details found on this website: https://cs.uwaterloo.ca/~csk/hat/ Print it in multiple colors, and get your kids hooked on infinite puzzles using…
The shape of these puzzle tiles was discovered and published by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss in “ An aperiodic monotile ” (March 2023, available at https://doi.org/10.48550/arXiv.2303.10798…
Closely following the Hat , Spectre is a shape for aperiotic tiling that does not need to be flipped. More details are in this arxiv preprint . There is a parametric openscad model to generate the tile (or multiple) with different…
It's one thing to play around with these in a 2D program, but it's way more educational to print a few out and place them together with your hands (they are only 4 CM across). Even though I made this model, I can't take any credit for the…
Have you heard about the Hat Polykite, the World’s First Aperiodic Monotile? It means this newly discovered 13-sided shape can tile a surface to infinity with no repeating patterns! On March 20, 2023, a group of computer scientists (David…
Hiding in plain sight: Wikipedia: «In 2023, David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss posted a preprint proving the existence of a tile which when considered with its mirror image form an aperiodic…
When printed on my Prusa MK3S w/MMU with the settings in the 3MF files, the tiles fit to the grid plate with a slip fit when oriented as printed, and with a snap fit when flipped. Tiles that snap in can be removed from the grid plate with…
Aperiodic monotiles are trending right now! :)) This one is not a real tile but it obeys the exact same logic and tiling constraints as the recently discovered “hat” aperiodic monotile. If you have not already seen what this is about,…
Many models appeared recently after the discovery of the aperiodic monotile family. More about the mathematics behind it here: https://arxiv.org/abs/2303.10798 Here's my interpretation of the “Turtle” variation, along with a Fish version…
D. Smith et al. recently discovered a shape, that can be tiled in infinite non-repeating pattern. This is known as the “einstein problem”. Not related to Albert Einstein, but instead focused on discovering single shape of tile ("ein…
A cookie cutter, whose shape is a remix of the world's first Aperiodic Monotile. Are you excited about math, and cookies? Well here you go. It is recommended you Print this cookie cutter using a Food Safe filament, and voilà- you can make…
I wanted to print dozens of these tiles so I thought I was efficiently organizing the tiles by neatly placing them together as a complete pattern in the slicer. I managed to get 24 on one sheet. Turns out… putting them into a simple 5x5…
I was having a hard time finding the shape in it's straight edged version shown in the paper: https://arxiv.org/abs/2305.17743
The hat is the first aperiodic monotile that has been discovered after decades of research. More details (and proof) can be found in this arxiv preprint .
This model is based on the work of David Smith, Joseph Myers, Chaim Goodman-Strauss and Craig S. Kaplan in their paper “An aperiodic monotile”. https://arxiv.org/abs/2303.10798v1
Explore the properties of the tiles and the limits of intuition, then generate a metatile and assemble. See. https://cs.uwaterloo.ca/~csk/hat/
The now famous spectre tiling has been seen many times on printables, here a version with an interesting drawing that never repeat ! Many information and sources here :…
I read about it on slashdot A nice article about it gave me the idea to create that shape as a printable tile. Have a look here [wikipedia.org]. It's called an einstein (from German for ‘one stone’) because it does the aperiodic thing…
Based on the aperiodic monotile discovered March 2023. see: https://arxiv.org/abs/2303.10798 There are two versions, only the border and filled with a sceleton. Printing without raft, not brim. Print Settings Printer Brand: FlashForge…
An aperiodic monotile was discovered in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. It is “a single shape which tiles the plane, and can’t be arranged to have translational symmetry.” The…
Remix of begineering's awesome version of the Aperiodic Monotile optimized for two-color printing on the Bambu printer. Color is added as a 1-layer inlay on the bottom of each tile half, which prints super-smooth on the High Temperature…
Remixed to include a hidden disk magnet. Use the included Fusion360 file to change the size of the magnet.
Tento tvar byl objeven v roce 2023 - https://arxiv.org/pdf/2303.10798.pdf Nepravidelná dlaždice pro stavebnici k pokrývání roviny. Aby bylo možné model mnohoúhelníku vytvořit, má tloušťku 2 mm, i když se jedná o rovinné útvary.
An aperiodic monotile was discovered in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. It is “a single shape which tiles the plane, and can’t be arranged to have translational symmetry.” The…
An aperiodic monotile was discovered in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. It is “a single shape which tiles the plane, and can’t be arranged to have translational symmetry.” The…
The moment I read this news, I knew I had to make a cookie cutter. Mankind will bake an incredible cookie to prove the endlessness of this hat pattern.…
Someone was looking for dxf of same, so uploading one, might delete later idk
This is a version of the “turtle” aperiodic monotile. It has the most helpful turtle trace area in the center, but that's not all! It can be really hard to draw aperiodic tiling without running into collisions or gaps. This stencil has a…
Update: The magnet attachment has been improved to use three 6×3 mm magnets. This allows the Einstein Hat to be used upside down as well. The single magnet on the top also makes the correct orientation of the tile easy to see. This…
Remix to add text. Scale as needed, but print copies at the same scale…..
What This is a set of coasters that have an in-laid aperiodic tile pattern. Why Aperiodic tiles are cool, and I don't have enough coasters. How The included 3mf project file contains three instances of same tile each scaled such that the…
Based on the shape discovered by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. https://arxiv.org/abs/2303.10798 This model has beveled grooves on one side which trace the trisected hexagons that can be used…
Chair44 — Experimental Geometric Relief A geometric relief model based on Chaim Goodman–Strauss’s Chair44 arrow markings. The markings are represented by tetrahedral bumps and dents. Where neighboring dents meet, their shared internal…
This is the same two-layer tile design in https://www.printables.com/model/928547-aperiodic-monotile-or-einstein-tile-with-hidden-ta but is reduced in size. Unlike the previous one it requires glue to assemble, but this can be done easily…
Einstein aperiodic tile in the "turtle" shape. the tile is relatively small to save space. 26 fit on the printbed of aprusa core one. It looks best when printed with two colors, one for the tile and one for the brim. It's easily possible…
Aperiodic Turtle Tiling Set — Tiles, Connectors and Hexagonal Board A hands-on tiling set with four free printable parts: a Turtle tile, a Trefoil tile, a straight connector and an optional hexagonal board. Rotate, flip and arrange the…
![Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi]](https://media.printables.com/media/prints/435459/images/3603903_5a1307db-843e-4e5d-8c95-e8c60ae24096/phi.jpg)
