Henry Segerman's Mathematical Art

Designs by henryseg
Contact Designer
Thank you for visiting my shop! Videos of many of the sculptures can be seen on the pages for the individual models, or you can visit my YouTube channel. See my website for non-3D printed artwork and other interesting things. Many of these sculptures are joint work with Saul Schleimer. Some of these feature our "maker's mark", shown here. I also have a second Shapeways shop, a collaboration with Marco Mahler to design 3D printed mobiles.

We found 100 products by henryseg

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Open book decomposition
by henryseg
 
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Regular triangulation of H³
by henryseg
 
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Knotted Cog (coloured)
by henryseg
 
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Triple helix
by henryseg
Some people were having problems with the gears being fused together on delivery, so I've altered the model. It is now printed disassembled, and you will need to put the gears into the frame before use.
 
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Triple gear
by henryseg

A smaller version of Triple Gear is available here. A baseplate and axle for using a motor to move the triple gear is available here. Also see 15 cm axle for Triple gear and 30 cm axle for Triple gear.

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 neighbouring gears must turn in opposite directions. Triple gear avoids this problem by having the three "gears" arranged like linked rings - the gears then rotate along skew axes, and the opposite direction rule no longer applies (although see also Oskar van Deventer's Magic Gears for another possible solution).

This is joint work with Saul Schleimer. We were inspired by another of Oskar's designs, his Knotted Gear, which consists of two linked rings that gear with each other, and of course we wondered if it would be possible to do three linked rings!

Here is a paper on the mathematics behind the Triple gear, and how we designed it.

A note on materials: I have so far printed it in White Strong & Flexible only. It may arrive with the rings slightly fused together, but gently moving them back and forth will loosen them up, and the mechanism gets smoother with use. I'm not sure what effect the polishing process would have on the gearing mechanism, since it would polish the exposed gear teeth but not those which are meshed as it comes out of the printer. So I have disabled the polished material options. If you really want to try it, let me know. I also haven't tested any of the "frosted detail" materials, but I imagine that they should work fine. It isn't printable in the other "detail" materials because of cleaning problems.

 
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30-Cell Puzzle
by henryseg

A large version of the puzzle is available here.

The goal is to assemble the five identical pieces shown in the first picture into the ring-like structure shown in the others. Each of the five pieces is made from six dodecahedral cells, giving the puzzle its name. It is based on the 120-cell, one of the six regular polytopes in four-dimensional space. When assembled the puzzle is a part of the stereographic projection of the radial projection of the 120-cell to the three-sphere.

Further description here: http://www.segerman.org/30-cell_puzzle.pdf.

This is joint work with Saul Schleimer.

 
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Hilbert Curve
by henryseg
A 3-dimensional version of the Hilbert space filling curve. As shown in the photos, if printed in one of the "Strong & Flexible" plastics, it can be used as a bracelet or hair accessory. It takes a little time to reform back as a cube after being stretched, but it seems that leaving it overnight does the job.
 
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Knotted Cog
by henryseg
This steampunk style knotted cog was procedurally generated using 3-dimensional spherical geometry, then stereographically projected into our (mostly) Euclidean universe.

Other sizes:
www.shapeways.com/model/231026/knotted_cog__large_.html
www.shapeways.com/model/231045/knotted_cog.html
www.shapeways.com/model/277265/knotted_cog__smaller_.html
www.shapeways.com/model/232385/knotted_cog__small_.html


 
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Sphere Autologlyph
by henryseg
A self-referential tessellation of the sphere.

This is a little delicate as the lines are 1.5mm thick, but it seems sturdy enough.
 
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Developing dragon curve
by henryseg
This design is based on an idea originally due to Geoffrey Irving (http://naml.us/~irving/).
 
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Developing Hilbert curve
by henryseg
 
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Developing terdragon curve
by henryseg
 
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Developing Sierpinski arrowhead curve
by henryseg
 
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Archimedean Spire
by henryseg
A ruled parametric surface based on the Archimedean spiral.
 
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Hopf Fibration 1
by henryseg
Rectangular tube version. One arc's worth of fibers, from pole to pole.
 
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Round Möbius Strip
by henryseg

The usual version of a Möbius strip has as its single boundary curve an unknotted loop. An unknotted loop can be deformed into a circle, with the strip deformed along with it.

In this version, the boundary of the strip is the circle in the middle, and the surface "goes through infinity", meaning that the grid pattern should extend outwards all the way. To save on costs, I've removed the grid lines that would require an infinite amount of plastic to print.

This was designed with Saul Schleimer.

 
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Round Klein Bottle
by henryseg
This is made by gluing two copies of the Round Möbius Strip along their boundaries. A Klein bottle in 3-dimensional space has to intersect itself, and in this case it intersects itself along a straight line. This was designed with the assistance of Saul Schleimer.
 
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Juggling Club Motion
by henryseg
This shows (a somewhat idealised version of) the path of a juggling club as it is thrown from one hand to the other. See http://shpws.me/a4k3 and http://shpws.me/a4kw for larger, hollow versions, the first suitable for printing in the "Strong and Flexible" materials, and the second for stainless steel.
 
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Juggling Club Motion (Large, for Stainless Steel)
by henryseg
This is a larger version of Juggling Club Motion (http://shpws.me/3V5k), and is hollow, with wall thicknesses large enough to permit printing in stainless steel. See http://shpws.me/a4k3 for a version with thinner walls, suitable for printing in the "Strong and Flexible" materials.
 
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3 Ball Cascade Motion
by henryseg
This is a "multiple exposure" style model, showing the motion of the 3 ball cascade juggling pattern. This design was suggested by Colin Wright.
 
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Mills Mess Motion
by henryseg
This is a "multiple exposure" style model, showing the motion of the Mills Mess juggling pattern. This design was suggested by Colin Wright.
 
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Seifert surface for (4,3) torus knot
by henryseg
 
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Seifert surface for (5,3) torus knot
by henryseg
 
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Seifert surface for (5,4) torus knot
by henryseg
 
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Seifert surface for (3,3) torus link
by henryseg
 
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Seifert surface for (4,4) torus link
by henryseg
 
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Space Filling Graph 1
by henryseg
This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, analogous to the fractal structure of a step in the construction of a space filling curve, but with greater connectivity. This greater connectivity makes the physical sculpture considerably more robust than the analogous sculpture of a step in the construction of a space filling curve would be. Each vertex at each step of the construction is degree 3, and is replaced at the next step by 8 vertices arranged in a 2 x 2 x 2 cube, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by 4 parallel edges. We begin the construction with the first step being the edges of a cube, and this is the result at the fourth step. The spacing between the vertices varies in order to highlight the fractal structure.
 
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30cm axle for Triple gear
by henryseg
This is an axle for the Triple gear (full size version).
 
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15cm axle for Triple gear
by henryseg
This is an axle for the Triple gear (full size version).
 
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Base plate and axle for Triple gear
by henryseg
This is a baseplate and axle for the Triple gear (full size version). The axle has a 5mm diameter hole in the bottom, for fitting onto a motor.
 
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Octahedron fractal graph
by henryseg
This is a graph embedded in 3-dimensional space as a subset of an "octahedral lattice", which is related to the tessellation of space using octahedra and tetrahedra. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 4, and is replaced at the next step by 6 vertices arranged in an octahedron, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by 2 parallel edges. We begin the construction with the first step being the edges of an octahedron, and this is the result at the fourth step.
 
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Cuboctahedral fractal graph
by henryseg
This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 3, and is replaced at the next step by 7 vertices which can be thought of as a subset of a 3 x 3 x 3 cubical grid, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by a single edge, joining to the vertex in the centre of each 3 x 3 face. We begin the construction with the first step being the edges of a cube, and this is the result at the fourth step.
 
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Fractal Graph 3
by henryseg
This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 3, and has the incident edges arranged either in a 'T' formation, or like a corner of a cube. The vertex is replaced at the next step by a subgraph of a 3 x 3 x 3 cubical grid, the choice determined by whether the edges meeting at the vertex are in the 'T' or 'corner' shape. Each edge is replaced at the next step by four parallel edges, joining to the midpoints of the sides of each 3 x 3 face of the 3 x 3 x 3 cubical grid. We begin the construction with the first step being three edges meeting in a corner formation, and this is the result at the fourth step.
 
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Fractal Graph 4
by henryseg
 
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Interlocking Möbius Ladders
by henryseg
 
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Clifford Torus
by henryseg
 
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Shop Details
Mathematical sculpture by Henry Segerman.

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