Replicator Constructions

George W. Hart

This page shows some models I have made with a Makerbot Replicator.  What's cool is that it can work with two materials simultaneously, and so has encouraged me to think about ways to emphasize pattern with color. Feel free to build, repost, and modify these stl files in any way you like, but please include a link to this page as your source. You may also want to see things I made on my Makerbot and things I made on my Thing-O-Matic. For more complex models that I have made on other 3D printing machines, see my Rapid Prototyping page.

Above is a hyperboloid with color used to emphasize how it is made of clockwise and counterclockwise segments.  To make your own copy of it, use these stl files for black and white.  As the image at the top of this page shows, it can be made directly on the platform with no raft and no support structure. It took a bit of scraping with an x-acto knife to clean up the random bits of ooze.  (There is a monochromatic hyperboloid on my Makerbot page.)  I like the way it looks like the black rods go through the white ones, but I also wanted to see an equal treatment of black and white, so I made this slight variation:

In this second hyperboloid, the black and white are treated equally, which gives a very different visual feel, even though it differs by just a fraction of a millimeter at the crossings.  This difference points out why it is important to pay attention to little details.  If you prefer this version, here are the stl files for black and white.

This is a spiky ball based on the (5,2)-Goldberg polyhedron.  There are 392 spikes sticking out on all sides.  380 of them are six-sided and twelve are five-sided. 

I designed it as two identical halves to be glued together.  The solid bottom gives it good adhesion to the build platform, so it does not come loose while building.

This rendering shows that many of the spikes are cut at the equator.  When assembling it, it is something of a challenge to get the correct rotation angle for a perfect match before the glue dries.  (Hint: align the grain of the plastic filaments.)  You can build a copy for yourself with these separate stl files for black and white.  When I built it, I set the black to 1% fill density and it came out fine.

Here's a sculptural treatment of the compound of five tetrahedra.  There are five identical tetrahedra concentrically interwoven through each other.  Each is white on the outside and black on the inside.  This is an ambitious build, because the nearly horizontal bars were built without support, so it is rather hairy under the arms, so to speak. The above photo is straight from the machine, still stubbly with stray ooze.

After cleaning it up a bit by scraping it with an x-acto knife, it looks much better. To make your own copy, you can use these stl files for white and black.

Here are the two halves of a hypothetical nautilus-like shell. My goal here was to comment on the common mis-conception that the nautilus has a golden ratio spiral.  A real nautilus doesn't.  This is what a nautilus shell would look like if it were based on a golden spiral.  I built it in halves on a raft, then glued the halves together.

The inside is a bit messy at the horizontal peak, but it isn't too bad after a light sanding, especially since people mostly see the outside.  You can see I designed the inside half of the shell's thickness to be all white, so there is a continuous inner layer for strength.  The black decoration is only on the outer half.

I'm quite happy with the final result.  There's a video explaining more about it here.  If you watch carefully, you'll notice the end of the raft started separating from the platform during the build, so I taped it down with some kapton tape. The files for the whole shell are here: white, black. I cut these in half, rotated the "bottom" half to lie in the +Z halfspace, then raised the black up by the raft thickness and built them using just a white raft.  Here files for the two halves, which you can use to build it this way, but before I raised the black by my raft thickness, i.e., these are registered to be built exactly on top of each other.  Build the two "top" ones together and then the two "bottom" ones together:

Here's a two-color mazzocchio. This is a polygonal torus which was a popular design for a hat in Northern Italy in the fifteenth century.  To make your own, here are the stl files for black and white.


Be careful not to mix centuries!

I tried making a Seifert surface based on the (2, 5)-torus knot but it didn't come out very well.
You might have better technique.  The files are here and here.

So I made a white one and...

...I painted the edge red.  The file is here.

Similarly, I made this Seifert surface based on the Borromean rings and painted the three links.
It looks really great!  The stl file for this is here.

Here's a design for a 12-part puzzle which is shaped like four concentric, overlapping triangles. Each triangle is composed of three identical parts. A wood version of this puzzle, called L'Etoile, was originally designed by Phillip Dubois and commercially available in the 1980s.  Not knowing what the interior of the pieces looked like, I could only hypothesize about the exact part shape on the inside where the triangular slabs overlap.

My first design used this part shape, in which each part locks around the outside of two neighboring parts.  The stl file is here if you want to make a copy, but I don't recommend it, because this design is very difficult to assemble and disassemble.

Then I saw a picture of the disassembled Dubois puzzle and saw how he cut the interior differently.  This is a small test model, and you can see big gaps in the joints, due to the part warping.  The gaps will shrink if you scale the parts up to about 150% from the stl file I used.

Finally, I made a larger version in two colors, adding a stripe to emphasize the four triangles. You can make a copy with these stl files for white and black.  It is a nice puzzle to assemble twelve parts into the four triangles. (Hint: first make modules using a few pieces, then combine the modules.)

Here are some patterned rollers based on M.C. Escher and ancient designs, which can be used to shape cookies or ceramics.

Chocolate cookies made with some of these rollers.  The stl files and detailed information are here.

Here is a set of five puzzles that involve rotational or screwing transformations in one form or another.

Here they are disassembled.  I put the STL files and description of them here.

I created this Venn Diagram Candy Dish as an exercise for participants in a course I am teaching to math teachers at Math for America in NYC.  The course is called "3D Printing for the Math Classroom."  Although this design is intended as an exercise for others to have practice in techniques for generating stl files, here's the stl file (11 MB) in case you just want to build one.

I then looked online and found someone else previously made a nice Venn diagram candy dish, produced by vacu-forming, not by 3D printing.  Check out Margaret Cumming's blog page to see how the compartments can be filled nicely.

Here's a two-color model of a sculpture Dual Planetoid by Bjarne Jespersen (who is undoubtedly the world's greatest mathematical wood carver).  In his version, he carved the two interlocking pieces out of a single block of wood and they are free to wiggle just slightly.  We were about to get together at a conference at which he was building a larger wood version of the design, so I thought I would make my own 3D-printed version to bring along. 

I adapted the design to be a puzzle with eight identically shaped parts that snap together.  The parts are not exactly 3-fold symmetrical.  One of the three prongs of each part has an extra octahedron and you need to position them thoughtfully to assemble it. Here is the stl file so you can make your own copy.  Print four copies in each of two colors to have eight parts total.   

Here's a very cool structure made of circles, related to the Schwarz minimal P-surface, as explained in this video.

The same object looks very different when viewed from other directions.  The (10MB) stl file is here.

(I have more to add here when I get time...)