Counting matching models…
This is a really simple jig that works about as well as the one I spent $9 for online, shown on its left. By “about as well” I mean that both require a lot of practice to use, and both still fail a lot for me. The welded filament will…
Some decorative items inspired by St. Patrick's Day, coming up soon as I type this. I printed these in white and applied green acrylic paint to the raised design by painting a flat surface and pressing it against. Alternatively, you could…
Description The 6x4x3 puzzle consists of one frame piece and four identical L-shaped pieces. Fit the 4 L-shaped pieces into the frame to create two different patterns, Hourglass or W-Toast, as shown in the photos. The total printing time…
There's not too much to say about this. I have been making crafts to celebrate Lunar New Year for a few years running and this is the first one I tried using 3D printing. Normally I work with strict geometries in Inkscape to make tiles…
This 7-piece 3D printed yin and yang is 40mm in diameter and fits together similarly to a burr puzzle. I was not trying to make a puzzle. I just wanted to make a multi-color object that I could fit together without glue. The inside…
These are Penrose kite and dart tiles that fit together like jigsaw pieces. Unlike jigsaw pieces, the holes are covered above, so after fitting them together, one side looks like a pure polygon tiling. It takes a little practice to rotate…
This is intended to be decorative, rather than illustrating any mathematical properties. It is based on a way of decorating Penrose kite and dart tiles to construct braids. You can find a model for printing separate tiles here:…
See Penrose kite and dart with Voronoi "cobblestone" surface for more information about what this tiling represents. Polymer clay makes the result look more natural and opens up other possibilities such as marbling. While more work is…
These tiles fit together like jigsaw pieces and hold when lifting when I print them in PLA on a Flashforge 3D printer. The tiles can be flipped between "S" and "Z" sides to make a variety of lozenge tilings. Strictly alternating will give…
I made some this design some time back to cut on a Cricut. It is based on a traditional spiral triskelion but with the spirals compressed into ellipses to match the curvature of the surrounding circle. The inner spirals look a little like…
These tiles fit together to make a variety of "lozenge" tilings, or tilings by 60°-120° rhombuses. Strictly alternating them like a checkerboard will give you a grid while keeping all the same orientation collects them into hexagons.…
These two triangular pieces are functionally the same as this earlier printable but keep the tabs hidden instead of making them visible like jigsaw pieces. Because the tabs need to be printed with overhang, they are given an upward slope.…
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…
Robinson triangles*, introduced by R. M. Robinson are another way to build a Penrose aperiodic tiling. https://tilings.math.uni-bielefeld.de/substitution/robinson-triangle/ They have the advantage of representing halves of kites and darts…
These tiles can be fit together as jigsaw pieces, and when assembled, will implement the elementary cellular automaton known as Rule 110 . They should ideally be printed in two different colors as shown, so that tiles representing a value…
Identical copies of this jigsaw piece, based on a hexagon, can be fit together at 120° rotations to implement an XOR function between neighbors, as shown: If you start with a single piece with an output of 1 (2nd or 3rd above) and…
I started with the tiles in https://www.printables.com/model/832714-penrose-kite-and-dart-covered-jigsaw and added raised sections on each tile that make complex braids when they fit together. They are primarily decorative and do not…
Robinson triangles, introduced by R. M. Robinson, are another way to build a Penrose aperiodic tiling. https://tilings.math.uni-bielefeld.de/substitution/robinson-triangle/ They have the advantage of representing halves of rhombs during…
This just another braid based on Penrose kite and dart tiles. It is purely decorative. You can see https://www.printables.com/model/1110175-decorative-penrose-tile-braid for a longer description of how it was made. It is not a Celtic…
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…
This is pretty self-explanatory but you will need some polymer clay skills to do a good job (and hopefully better than I did in the photo). Roll out some polymer clay as flat as you can, about 3mm thickness. Use the cutter to split it up…
This more of a prototype than a real design. I plan to work on more coasters, tiles, and resin molds using this idea, but it came out interesting enough to post. The Belousov-Zhabotinsky reaction is an oscillating chemical reaction that…
These 19 tiles (with alternates) fit together like a puzzle, but the only way to complete it with a boundary is if it represents a still life in Conway's Game of Life, using dark blue circles for live cells. The photos shows 3D-printed…
These are Penrose rhomb tiles that fit together with hidden side snaps to enforce matching rules and to hold the tiles together into a liftable layout. When assembled, only the polygons show both top and bottom. This is similar to…
I saw this cover on the street while in Galway and was impressed by the artistry of such a functional object. It is less than a foot across and probably intended to cover a water valve or meter. I saw a few others like it. Most of the…
This can be thought of as one of the slowest ever implementations of a cellular automata (CA), in this case, "Critters" a reversible block cellular automaton discovered by Tommaso Toffoli and Norman Margolus. See…
This is the same design as Penrose tiling based on flippable triangles with hidden tabs but with a layer on top and bottom with narrow grooves that fit together as braids when the tiles are placed. You can go to the original link to read…
These five tiles fit together like jigsaw pieces and can be used to explore 2-state Moore neighborhood cellular automaton, the most famous example being Conway's Game of Life . Note: the tiles are shown with two colors for clarity though…
You can find a lot of printable pentomino sets. I just felt like making my own design and keeping it as small as I could get it. I could probably print smaller than the 3mm grid pentominoes, but it is about the limits of usability for me.…
This is a rework of https://www.printables.com/model/882253-sierpinski-triangle-xor-jigsaw-pieces , which is based on 2D jigsaw fittings. The new one has side snaps that are hidden when assembled. Identical copies of this snap-fit piece,…
These tiles are based on the seven unique polygon cells of the Voronoi diagram of a Penrose rhomb tiling . See my previous design for more explanation. My goal is not primarily a mathematical puzzle, but a fun (I hope) way to plan…
This is part of a work in progress in which I intend to use a face-centered cubic packing to embed block cellular automata rules. https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres There are other shapes like it in Printables…
This is similar to the tiles in interlocking rhombus tiles but includes a complex seamless texture based on the Belousov-Zhabotinsky reaction. The surface was computer-generated using boundary conditions consistent with 120 ° rotation and…
Similar to https://www.printables.com/model/832711-interlocking-rhombus-tiles but using hidden tabs instead of interlocking jigsaw pieces. These can be laid out to form a variety of so-called lozenge tilings, which can also be interpreted…
This design is similar to an older printable of mine and you can read more about Penrose kites and darts there and on the Wikipedia page. The main change is that the tabs that hold the tiles together are completely internal. They have a…
These are Penrose kite and dart tiles that fit together with hidden side snaps to enforce matching rules and to hold the tiles together into a liftable layout. When assembled, only the polygons show both top and bottom. The big challenge…
These are the 22 pieces omitted from the earlier Connected curves puzzle . Unlike those 20 tiles, which each had 3 connected components, these have 1, 2, 4, and 5 components. To get a closed curve without holes, the total number of…
This print is a master for a silicone mold of a decorative triskelion shape that I made in green for St. Patrick's Day. The print itself isn't the final product, just its shape prepared to fill with silicone. You need additional material…
These are symmetric patterns generated using a Gray-Scott reaction-diffusion system with hexagonal geometry and boundary conditions for various choices of parameters shown in the image. Each hexagon tiles with itself seamlessly, but they…
This is a reworking of https://www.printables.com/model/948066-penrose-tiling-based-on-flippable-triangles-with-h with a slightly different approach. That link has more details. The tiles are the same size, but incompatible. I have…
Similar to my previous model of rhombus tiles but smaller (10mm on a side instead of 12mm) and with improved snaps. These can be laid out to form a variety of so-called lozenge tilings, which appear as orthogonal projections of stacks of…
A revision of https://www.printables.com/model/832708-conways-game-of-life-still-life-tiles using hidden snaps instead of jigsaw like fittings. These 19 tiles (with alternates) fit together like a puzzle, but the only way to complete it…
By itself, this is a 3D print of elliptical Borromean rings represented as grooves, and you can get then in a different color by switch filaments. The real purpose, though, was a proof of concept for applying detailed inlays of cardstock…
See https://conwaylife.com/forums/viewtopic.php?f=12&t=4300&p=135096 for a more detailed explanation. The curves in these tiles are based on parentheses matching, and pull in surprisingly many concepts from combinatorics and graph theory.…
A puzzle similar to a 14 piece puzzle that I posted in another printable. You can find more of the theory in that write-up. The puzzle consists of 20 semicircles that snap together. Each semicircle has a set of three curves than can be…
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…
I updated the photographs since the originals did not print well. For some reason my printer leaves a lot of threads as it moves between the small spots on each layer. Lowering the print temperature helped, but other adjustments had…
Decorative designs for the Year of the Horse 2026. The rectangular design has an AI-generated image and the circle has an AI-modified image based on Galloping Horse, Xu Beihong 1953. See…
There are two printable objects: a hexagonal base and a rhombic color cap. Each base has 3 spots for caps, which should be printed in different colors. Attach the caps to the base upside down by sliding the tabs under the center divider…
See https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres for a discussion of regular sphere packing and the lattices that result. These components: cube and tetrahedral joints, along with equal-length struts, fit together into…
These tiles fit together like jigsaw pieces and will hold rhombic dodecahedrons in position for the two standard orientations of a face-centered cubic sphere packing. The pictures are self-explanatory. I didn't try to make the base…
This is much like other Penrose Voronoi projects I've done but it's one piece, not a set of tiles and was generated using a Python program and some additional steps using imagetostl . You can read more about how I made it at this link ,…
A variation of snap fit Penrose kite and dart tiles that fit together the same way as the earlier design. See that link for more details. These tiles have a surface texture based on a Voronoi diagram made by intersecting flattened…
This is related to some other recent printables I have done of Penrose tiling Voronoi diagrams. You can see a longer explanation here . Instead of tiles, these are ink stamps. The photos show some examples of the kinds of patterns you can…
This is like my triskelion in that the 3D print is not the final result but the first step in the process. I have streamlined this into the easiest resin project I could come up with. The most complex part, assembling the tesserae , is…
This began some time back when I found that the cleaner attachment for my Zyliss garlic press stopped working. Through careless use I had bent some pins and it only got worse from there. It was not hard to reverse engineer the geometry…
This came out of a long effort to make a pattern resembling brain coral from a discrete process. The idea I settled on was to fill a hexagonal grid with cells such that: Each filled cell has exactly two filled neighbors in the ring around…
There's not much to say that I haven't said already in the description of more ambitious designs like Penrose tile set with hidden snap fittings . These are simply flat pieces that assemble like a jigsaw puzzle. They print at 2mm height…
For a longer description of Penrose kite and dart tiles, see one of my previous printables such as this one with hidden snap fittings . There is also a detailed wikipedia page on Penrose tiles . This model contains three kinds of…
These are similar to some other designs such as Checker Penrose tile triangles , Penrose tiling based on flippable triangles and Flippable Robinson triangles but I have reduced the size significantly. You can see the photos comparing them…
Note: I have put the original models up on Tinkercad where they can be edited. Overview This is a more ambitious follow-up to my Penrose Voronoi suncatcher . Instead of providing just one design, it is a set of pieces that fit together…
See this wikipedia page for an introducing to Game of Life and gliders. This is purely a decorative design for Life enthusiasts, but it is east to print and use if you have silicone and epoxy resin. You can find a more detailed…
A Wieringa roof is a three-dimensional extension of Penrose rhomb tilings with the remarkable property that it is composed only of golden rhombuses, those with an aspect ratio equal to the golden ratio. Instead of lying flat, these…
This is a follow up to modular pieces for constructing Wieringa roofs , a way to represent a Penrose tiling , which you can read about elsewhere. In this design, the only pieces you need to print are the plastic clips that hold flat…
These are all currently available results.
