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These parts make an expanding recursive mechanism. The file contains four boxes and eight racks, with equal numbers of each handedness of boxes and racks. The parts are designed to be held together with M3 bolts (16mm long). By combining…
This is an expanding mechanism: it goes from small to big, and it has one degree of freedom. In the first photograph, the two triangles are identical copies of this mechanism. The green triangle is fully expanded, while the white triangle…
This design is made out of shapes called cyclides . In this mechanism the cyclides rotate against each other, opening out while staying in contact so that the overall shape transforms from a sphere to a disk. This design was discovered by…
This model is featured in figure 3.12 of Visualizing Mathematics with 3D Printing . Video . Stereographic projection is a map from the sphere to the plane: Imagine straight lines going from the north pole of the sphere down onto the…
A cube of bevel gears. Joint work with Sabetta Matsumoto. Sometimes designs like this are called “brain gears”. To make this, you will need two copies of the half core, eight copies of the gear and its cap, twelve M2 nuts, four 16mm M2…
Video . In this unusual mechanism three gears mesh together in pairs, and yet they can turn! If you take three ordinary gears and put them together so that each gear meshes with the other two, then none of the gears can turn because…
A "geared" mechanism in which the two gears move with screw motion. I've included the “gear” part, of which you will need two copies, and two versions of the “cage” part with different amounts of clearance around the gears. Depending on…
In this symmetric mechanism, moving any of the twelve sticks into or out of the core moves all of the others. The force is transferred around the core by gears meshing with racks on the sticks. To build this you will need twelve copies of…
A version of the Ames room at a scale that works for Lego minifigures. If you put a camera 100 mm from the center of the undistorted version of the room then it looks identical to the distorted version of the room. There is a base with…
This is a geared mechanism that transforms shape. The twelve edges are geared together so that they all simultaneously rotate 90 degrees, transforming from a cube shape into an octahedron shape and back again. The edges extend in length…
A mechanism consisting of a pair of bevel gears for each edge of an octahedron. Joint work with Sabetta Matsumoto. This design uses bolts for the axles of the gears. To make this, you will need two copies of the half core, twelve copies…
An object that looks like a square from one direction, and a circle from another.
A kinetic artwork consisting of a deployable grid of scissors. Joint work with Kyle VanDeventer. As well as the print, you will need the following metric nuts and bolts: M3 8mm long x 23 M3 10mm long x 3 M3 12mm long x 16 M3 locknut x 42…
Extra parts to add to an injection molded extensors kit (available from http://www.mathmechs.com ) to make an extensor grabber toy. Designed by Will Segerman and me. The plunger comes in three parts. The shaft part (with one thumb hole)…
An optical illusion shows an impossible triangle when viewed from the correct direction.
An optical illusion shows an impossible triangle when viewed from the correct direction.
This model is featured in figure 4.5 of Visualizing Mathematics with 3D Printing . Category: Math
Video . This is another moving geared thing, joint work with Saul Schleimer. The three pins can move against each other, but must all move together - no one pin can move on its own. Borromean hairpins is also available at Shapeways .…
This model is featured in figure 7.4 of Visualizing Mathematics with 3D Printing . Category: Math
All 92 Johnson solids. These are the strictly convex polyhedra that can be made from regular polygons, excepting the platonic and archimedean solids, and the prisms and anti-prisms.
The gears in this mechanism force each neighbouring pair of arms to have the same angle between them. This angle alternates between turning to the left and turning to the right, so the mechanism acts exactly like one half of an ordinary…
This model is featured in figure 3.13 of Visualizing Mathematics with 3D Printing . Category: Math
Print the two halves and then glue them together to make a sphericon, which will roll in a zigzag motion.
This model is featured in figure 5.4 of Visualizing Mathematics with 3D Printing . This is joint work with Keenan Crane. Category: Math
Two sticks with racks can mesh into each other and transfer movement into a different direction. Thanks to Sabetta Matsumoto for the idea to have an image of the rack on the front of a stick also appear on the back. This makes it easier…
A model of (one version of) the mechanism inside a Rubik's cube. You will need one core, six copies of the face parts and face caps, twelve edge parts and eight corner parts. To fasten the faces onto the core (through the face caps), you…
This is a building system for making mechanisms which can change size. The parts can be built out to make expanding mechanisms of varying sizes and shapes. The simplest version of this mechanism is a "right-angled hexagon" - six of the…
These models are featured in figure 2.9 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 2.6 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 3.14 of Visualizing Mathematics with 3D Printing . Category: Math
A larger version of this model is featured in figures 4.13 and 4.14 of Visualizing Mathematics with 3D Printing . This 3D printed illustration of the hyperbolic plane is joint work with Saul Schleimer. The hyperbolic plane has constant…
These gripping gears mesh with and rotate around each other, but with no axles and no frame. This version has "pass-through" holes, that allow a solid object (e.g. a screwdriver) to pass between the gears. YouTube video:…
Video . This is joint work with Saul Schleimer. After making Triple gear , we realised that there is a much easier way to design a mechanism with three pairwise meshing gears! Triple helix is also available at Shapeways . Category: Math Art
Print the two halves and then glue them together to make a “three-cone” sphericon, which will roll in a zigzag motion.
This model is featured in figure 4.23 of Visualizing Mathematics with 3D Printing . Category: Math
This is a linkage that transforms shape. Two of its states are a cube and an octahedron, passing through a cuboctahedron state. It also has other shapes that it can fall into, which makes it a bit of a puzzle to work out how to make it go…
This model is featured in figure 4.6 of Visualizing Mathematics with 3D Printing . Category: Math
Stages of the development of the dragon curve fractal, extruded through space. Category: Math Art
This model is featured in figure 2.8 of Visualizing Mathematics with 3D Printing . Category: Math
This is joint work with Saul Schleimer. A torus link is a link that can be drawn on a torus. A Seifert surface spans its link, somewhat like a soap-film clinging to its supporting wire-frame. The surface acts as a bridge between the…
This is a compilation of Jason Cantarella 's ropelength minimising knots, arranged into a single file for the thin versions of the knots, and a single file for the thick versions. These are all of the prime knots with at most 7 crossings.…
Four identical parts go together to make a symmetric sliding mechanism. It is a difficult puzzle to put them together, and even more difficult to have them slide together so that they all have the same offset relative to each other. This…
A half cube prototype for the Helix cube puzzle, showing the mechanism.
This model is featured in figure 4.21 of Visualizing Mathematics with 3D Printing . This is joint work with Roice Nelson. Category: Math
These models are featured in figure 6.2 of Visualizing Mathematics with 3D Printing . Category: Math
Buckminster Fuller invented the jitterbug, a linkage made from eight triangles, connected at their vertices in such a way that it can expand from an octahedron into a cuboctahedron shape and then contract again back to an octahedron. The…
This model is featured in figure 4.23 of Visualizing Mathematics with 3D Printing . This is joint work with Roice Nelson. Category: Math
This model is featured in figure 6.16 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 6.10 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 5.11 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 3.31 of Visualizing Mathematics with 3D Printing . This sculpture was inspired by a question of Vi Hart . As far as we know, this is the first sculpture (in fact, physical object) with the quaternion group…
This model is featured in figure 5.5 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.22 of Visualizing Mathematics with 3D Printing . This is joint work with Roice Nelson. Category: Math
This model is featured in figure 6.12 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figures 4.13 and 4.14 of Visualizing Mathematics with 3D Printing . This is joint work with Saul Schleimer. A smaller version is available here . Category: Math
This model is featured in figure 4.8 of Visualizing Mathematics with 3D Printing . This is joint work with Geoffrey Irving. This was printed on an SLS machine. I have no idea if it will work on other kinds of 3D printer. Let me know if…
This model is featured in figure 3.34 of Visualizing Mathematics with 3D Printing . Category: Math Art
This model is featured in figure 5.7 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.10 of Visualizing Mathematics with 3D Printing . Category: Math
Panels to print and insert into a Holonomy genus two surface, available from http://shpws.me/TeEf The photo shows desktop 3D printed panels inserted in a frame printed on an SLS machine, together with an SLS printed “rook” piece.
This model is featured in figure 5.6 of Visualizing Mathematics with 3D Printing . Note that I digitally modified the photograph of the model shown here to colour the knot. Category: Math
This model is featured in figure 4.3 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.2 of Visualizing Mathematics with 3D Printing . This is joint work with Geoffrey Irving. This was printed on an SLS machine. I have no idea if it will work on other kinds of 3D printer. Let me know if…
This model is featured in figure 6.13 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.9 of Visualizing Mathematics with 3D Printing . Category: Math
Douglas Hofstadter calls this kind of sculpture a “trip-let”, presumably because it contains three ("trip") letters ("let"). Video: https://www.youtube.com/shorts/8xu6FO0ETcI
Any finite part of this fractal knot can be untied, but the full infinite fractal knot cannot! (Not all of the infinitely many loops are included in this model.)
This model is featured in figure 5.12 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.18 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 6.21 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 6.25 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 5.6 of Visualizing Mathematics with 3D Printing . Category: Math
These models are featured in figure 6.1 of Visualizing Mathematics with 3D Printing . Category: Math
These models are featured in figure 3.24 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 4.19 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 1.16 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 6.18 of Visualizing Mathematics with 3D Printing . Category: Math
These show a selection of the spherical symmetry groups - the ways in which an object can be symmetrical by rotating about and reflecting through a central point. See the wikipedia page for more details, or better, the book The Symmetries…
This model is featured in figure 4.17 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 3.33 of Visualizing Mathematics with 3D Printing . Category: Math Art
This model is featured in figure 1.19 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
The hyperboloid of one sheet is a surface that often shows up in multivariable calculus classes and in the shape of cooling towers of nuclear reactors. Perhaps surprisingly, there are two families of straight lines in the hyperboloid.…
This model is featured in figure 6.20 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 1.29 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This model is featured in figure 1.24 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
These models are featured in figure 6.14 of Visualizing Mathematics with 3D Printing . Category: Math
This model is featured in figure 3.15 of Visualizing Mathematics with 3D Printing . Category: Math
These models are featured in figure 4.4 of Visualizing Mathematics with 3D Printing . Category: Math
These models are featured in figure 6.17 of Visualizing Mathematics with 3D Printing . Category: Math
Numerals to print and inset into tiles for the Hyperbolic 29 Puzzle (available from Shapeways at: http://shpws.me/SJra ) Category: Puzzles
This model is featured in figure 1.26 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This model is featured in figure 1.23 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This model is featured in figure 1.28 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This model is featured in figure 1.25 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This model is featured in figure 1.27 of Visualizing Mathematics with 3D Printing . See also Solid comma symmetry spheres . Category: Math
This is the logo my collaborator Saul Schleimer and I add onto our models. It is a 2-dimensional stylised picture of the Whitehead link , a key example from our research area, 3-dimensional geometry and topology. It also resembles our…
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