# Discover » Art » Mathematical Art

by Bathsheba
The best triply periodic minimal surface ever!

I put a bigger one here.

(193)
•
From: \$16.99

by Bathsheba
A Klein bottle.
Warning: this Klein bottle does not open beers, it just looks cute.
The Klein Bottle Opener is here on Shapeways or here on Bathsheba.com.
A bigger bottle is here.

(86)
•
From: \$18.18

by TerraCotta
If M.C. Escher had owned fidget toys, he would have worn "One ring to rule the ball" as a pendant. A single, continuous line contains a small ball that makes orbit after mesmerizing orbit but cannot escape, always held down in four directions. Available in solid, durable stainless steel with optional antique bronze and gold plated finishes to fit any context, "One ring to rule the ball" now also includes a free rubber necklace so that you can confuse your mind any time the fancy strikes you! One customer echoes many others in saying, "I couldn't put it down. This thing is just too fun!"

(51)
•
From: \$19.04

by Bathsheba
Another projection of the 4-dimensional hypercube, this one close to vertex-centered. I love the shape of its hull: almost a rhombic dodecahedron, but skewed just enough to keep the central vertices from meeting.
The more usual projection is here, other polytopes are here.

(45)
•
From: \$23.71

by Bathsheba
A theorem walks into a bar...
The Klein Bottle is a mathematical joke: a surface with only one side. This one feels just right in your hand and opens bottles with ease and style. Built to last in steel, it's the perfect touch for any math fan's kitchen.

Yes, it really works!

Klein not-a-bottle-opener is here.

(23)
•
From: \$77.00

by Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the fifth, the hyperdodecahedron, a remarkably beautiful object brought to my attention by George Hart.

Here it's shown in a Schlegel diagram so you can see all 120 dodecahedral cells, though most are transformed by perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.

A bigger model is here.

(26)
•
From: \$16.62

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.

(20)
•
From: \$25.00

by Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the fifth, the hyperdodecahedron, a remarkably beautiful object brought to my attention by George Hart.

Here it's shown in a Schlegel diagram so you can see all 120 dodecahedral cells, though most are transformed by perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.

A smaller model is here.

(46)
•
From: \$59.12

by Bathsheba
A pendant for metal printing.  I think this may be the most adorable thing ever.

(15)
•
From: \$5.90

by ShapeKays
This is a model of the woodcut picture made by M.C. Escher in 1965 called 'Knots".
It has since then been a challenge for 3d modelers and mathematicians.
As far as I know it has not been modeled in 3d up till now. (It has! see comments).

The model's height is about 8 cm.

(20)
•
From: \$14.78

by Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the third, the hypercube or tesseract, in the classic projection into 3-space, showing its 8 cubic faces in a nice straightforward visualization.
A different projection is here.

(35)
•
From: \$21.74

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.

(5)
•
From: \$40.00

by Bathsheba
A delightful surface: the gyroid put through a simple inverse transformation. It's ellipsoidal on the outside, and there is a sphere taken out of the center, which is difficult to see; for otherwise it would be infinitely tiny inside, and therefore unprintable.

(23)
•
From: \$48.97

by Wahtah
A Sierpinski tetrahedron, the 3D version of the Sierpinski triangle, stage 5 I think. There are 4096 of the smallest tetrahedrons. The model has 499994 faces.

Update:
The edges are now almost 18 cm (7 in) long and it stands about 14.5 cm (5.7 in) high.

The model has been updated because the smallest struts were a bit too small to be printed. So it's now 1.5 times bigger in all directions.

The pictures are of the previous smaller version, the new version has been ordered successfully a number of times in WSF.

I created the model using POVray and MeshLab.

(2)
•
From: \$48.94

by SteveWinter

Roll a Ball on Plastic Rails Inside a 3D Cube. Reach the Exit to Solve the Maze Puzzle. Rolling Ball Maze Puzzle & Brain Game for Kids, teens & Adults.

New 3D Rolling Ball Maze Puzzle. Roll the ball inside a Plastic 3D maze cube to the exit to solve the puzzle. New 2011 brain toy game. A Work of Art.

Color and material options are in the "Select Material" drop-down list on the right. If you want an option not shown or would like a quantity discount, please click on the "Contact Designer" button to write me an email.This pack includes the mazes listed below. Each maze includes it’s own ball.

Escher’s Playground - Reminiscent of the upside-down staircase paintings by Escher, this 7x7x7 maze will soon have you forgetting which way is up and down. The dimensions of this maze are 40mm by 40mm by 40mm and the ball is 9mm in diameter.

Floating Labyrinth - The ball appears to float through an intricately connected matrix. What appears to be open paths are mysteriously blocked in this 6x6x6 maze. The dimensions of this maze are 31mm by 31mm by 31mm and the ball is 8mm in diameter.

Zig Zag Zog - You will learn to zig zag in three dimensions to solve this 5x5x5 maze, but watch out for the pitfalls! The dimensions of this maze are 24mm by 24mm by 24mm and the ball is 7mm in diameter.

Start by pushing the ball into the spring loaded entrance ( it looks like a backwards “J”). Tip the maze in different directions to roll the ball along the paths through the maze. Don’t worry, if you make a wrong turn, the ball will not fall out of the maze. If the ball runs into a dead-end you can just roll the ball back the opposite way and try another path, that’s all part of this fun brain game. When you reach the exit there is a spring loaded button to press to release the ball from the maze. The exit is in a corner of the 3D maze, where you will find a bar with the little button sticking out from the side of the maze.

Each maze game come with the ball attached by a little chain link cage for shipping. This needs to be cut off and cut open with scissors and the ball will fall out. Note that each larger size maze comes with a larger ball. The balls can quickly and easily be colored with a highlighter or marker. Let the ball dry for a minute after applying then roll between clean white paper to remove excess color so it does not rub off on the maze. Paint for plastic models can also be used. The orange, green and black balls in the pictures were colored with highlighters or markers. Coloring the ball makes it easier to track in the Labyrinth maze.

See for yourself how Ethereal Maze Puzzles take maze puzzles to a whole new level of challenge and fun. With their convoluted lattice structure they can also be enjoyed as captivating and intriguing sculptural works of art.

Show off these unique Works of Art in a quality display case. The medium size case is about \$3 and is perfect for "Escher’s Playground". You can see a picture of the display case with a maze inside in the photos above. Use the link below to get your Display Case with Free Shipping.

Medium Size BCW Maze Puzzle Display Case

If you are in the UK you can get a similar one for about GBP 5.30 with Free Shipping with the link below:

Display Case for Bare Bones for UK Customers

(19)
•
From: \$17.99

by MindEversion
A borromeanring-minimal surface in honeycomb style. Now i have one in a half size too.

(23)
•
From: \$102.68

by virtox
Phamora Ceramics!

Is inside out? Or is it not? Perhaps both?
This is an Amphora from another space-time.
An ancient object which we knew had to exist.
And after years of excavation in other dimensions we finally found it!

A very exotic vase with a unique near-impossible shape, suitable for use with dry flowers and striking enough to stand alone.
Theoretically it can also hold water in the toroidal bottom part, read practical details below.

Very suitable as a wedding gift to symbolize love and infinity.
The number eight (or sideways infinity) plays an important role in this piece,
both in the number of arms and the cross-section of this model.

Notes:
To improve print quality and after some deliberation with production, this model has been slightly updated on August 24th 2012; The arms have been thickened and the holes enlarged to improve strength and glazing.
Still I recommend not to put a lot of stress on the handles.
Refer to rendered images for the latest version. I will update photo's asap.
The bottom it stands on, is unglazed, which is invisible during normal display.
All clearly visible parts will be fully glazed, but there is a chance some parts on in the inside might not, which may compromise it's ability to hold water.
While production does their absolute best and all recent prints turned out perfectly glazed and hold water, due to the complexities involved, there is no 100% guarantee for to be absolutely watertight.

(8)
•
From: \$135.30

by Bathsheba
A four-dimensional cube at pendant size.  Is it adorable?  Why yes, it is. Some feel it is a little large to wear as jewelry, so I've uploaded a smaller one here.

More polytopes are here.

(13)
•
From: \$6.66

by Bathsheba
It's a little hypercube pendant! There is a slightly bigger one here.

(2)
•
From: \$4.94

by schaewill

(18)
•
From: \$35.88

by Oskar_van_Deventer
CAUTION: FOUR SPECIAL EDGES ONLY. Anisotropic Cube is a modification of Oskar's Gear Cube that is being sold by Mefferts.com. Buy a Gear Cube and replace four of the gearing edges by these four pieces. The result is a puzzle that has all the gearing fun of Gear Cube, but much harder to solve.

Read more at the Twisty Puzzles Forum

These are just the four special pieces. If you want to buy the full puzzle, assembled and sticked, then search the internet for Mefferts and "Gear Cube Extreme".

(18)
•
From: \$31.00

by joabaldwin
A compound mobius strip created out of 36 interlocking mobius strips.

All segments are thin mobius strips, and they weave and interlock perfectly through the spaces left between them. Highly complex, and a headache to look at, yet it possesses an inherent mathematical simplicity and beauty.

This model is 3d printed out of a sintered vinyl plastic, which makes it very resilient and bendable. It won't break if you drop it.

(2)
•
From: \$27.00

by MikeNaylor
A surprising arrangement of figures to create a mathematical form.

Please note that you must order TWO SETS to create the cube – each set includes two figures and four are necessary to create this sculpture. The figures are identical and snap together tightly hands to ankles to make this striking sculpture. Mix and match colors for your own effects. Or order more than two sets to experiment with other configurations.

This model is being exhibited at the Center for Arts Gallery at Towson University, June 30-July 28, 2012.

(6)
•
From: \$39.81

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.

(10)
•
From: \$21.99

by schaewill
The sizing for this ring is between a 7 and an 8

(12)
•
From: \$3.20

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

(5)
•
From: \$9.92

by quirxi
This is one of Escher's tesselating fishes in 3D. Several of these fishes can be grouped together, so that they form a never ending pattern.

(10)
•
From: \$3.31

by Bathsheba
The same as this model on bathsheba.com: here it is in some other materials.

Bigger version here.

(2)
•
From: \$7.31

by Bathsheba
The BBC feature The Code, which aired in the summer and fall of 2011, culminated in a treasure hunt. This is the treasure. The original was made in bronze-finish steel and silver; this recoloured model shows the structure. It is a rendering of the five Platonic solids, nested.
An uncoloured version is here.

(2)
•
From: \$31.16

by jayfisher
A detailed full color model of each of the first six planets (out to Saturn) and major moons of the Solar system, to (logrithmic) scale.
(Note: the full Solar System set of planets and moons is available as a set here)

All surfaces are reproduced from NASA imaging.
For size reference, Jupiter is 22mm (0.9 inch) diameter, and Earth is 11mm (0.45 inch) diameter.

This set is designed for use in orrery or other models of the solar system, and so to best present all planets while preserving scale, the scale has been compressed - a logrithmic scale instead of a linear scale. This means that if the model of a moon of Jupiter is larger than the model of Mercury but smaller than Mars, then you know that the real moon really is larger than Mercury and smaller than Mars, But the size diference is compressed - Jupiter, which is really more than ten times Earth's diameter, becomes only twice Earth's diameter, etc. This logrithmic scale allows all planets to be clearly visible together, while at the same time still indicating their sizes relative to each other.

The set contains six planets, and nine moons:
[In order of appearance in the photo above, right to left]
Mercury
Venus
Earth
- Moon / Luna
Mars
Jupiter
- Ganymede
- Callisto
- Io
- Europa (attempt no landing there)
Saturn
- rings of Saturn
- Titan
- Rhea
- Iapetus
- Dione

All objects have a 1.3mm (0.05 inch) hole at the south pole, about 3mm deep, for a brass axle (or a toothpick).

What color is a planet - is it color of its surface materials, or the colour of its atmosphere from space, or the color of the surface being colored by the atmosphere filtering light from the sun? The appearance in this set attempts to be that of the surface with moderate atmospheric influence, (with the gas giants depicted as the atmosphere and surface being the same thing). For example, this means that Venus depicts the features of its surface, but they are tinted somewhat by its atmosphere. Similarly, Earth and Titan show ground features, but some areas are tinted and obscured by atmosphere.

In areas where the model surface is more detailed than the most detailed NASA photography, the overall surface appearance conforms to what is known, but finer textural details are speculative. (Or, if there is an atmosphere, it is shown as particularly thick and opaque over the unmapped area.)

Due to hard limitations of the Shapeways 3D printer, the moon Dione is using the surface map of Rhea. I chose Dione because the surface is very similar to Rhea, and it is the most minor moon in the set. The alternative was simply to remove an object, but I preferred the set to include four of Saturn moons, like it does for Jupiter.

(9)
•
From: \$22.11

by TerraCotta
This beautiful design is a level 2 approximation to a Menger Sponge, measuring 1.4 cm on each side and suitable for use as a pendant or small and stylish paperweight/knicknack. Available in solid, durable stainless steel for lasting quality. Matching earrings available at http://www.shapeways.com/model/74647/level_2_menger_earrings.html

(14)
•
From: \$9.13

by Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This one is the odd polytope out, the one without a 3D counterpart.

It has 24 octahedral cells, all shown in this Schlegel diagram. Like the pentachoron it's self-dual -- the only self-dual solid in any dimension > 2 that is not a simplex. And if that wasn't enough, it's also the only regular convex polytope in any dimension > 2 that tiles its space and is not a hypercube.

(2)
•
From: \$16.70

by unellenu

Snowflake fractal pendant or decoration, pictured in white, strong and flexible.

This design looks beautiful worn as a pendant, and can also be hung as a tree ornament.

Dimensions of the pendant are cm:4.75 w x 4.908 d x 1.332 h / in:1.9 w x 1.9 d x 0.5 h (the dimensions of every Shapeways model are also on each page - near the bottom of the page).

The unellenu store on shapeways - for designer objects, fractal art, sculpture and jewelry.
shapeways.com/shops/unellenu

unellenu website
http://unellenu.com

Save

(4)
•
From: \$18.00

by unellenu
Julianna fractal lace,  fractal model, with a loop at the top for hanging.
Wear as a pendant , hang it on a wall, or near a window.

15.3cm X 9.5cm

The unellenu store on shapeways - for designer objects, fractal art, sculpture and jewelry.
shapeways.com/shops/unellenu

(3)
•
From: \$21.00

by virtox
While provocatively curved, she is indeed very shy!
She only allows a glowing glimpse of what she holds inside.

A light shade for LED tea-light or Luxeon/Cree LED
Hiding the source from direct view, resulting in a gentle light emerging

Limited edition
This is the original design, at nearly 20cm high, with 2mm thick walls it is costly to produce.
To compensate, only ten will be produced, currently only six are still available

More
Other sizes and shapes available.

(27)
•
From: \$250.00

by Bathsheba
The Schwartz D ("Diamond") surface is a triply periodic minimal surface, like the Gyroid. Here it's been translated in both normal directions, and one of the two resulting (identical!) surfaces networked. Another Schwarz surface is in metal here: http://bathsheba.com/math/schwarzd.

(21)
•
From: \$77.98