# Discover » Art » Mathematical Art

by Oskar_van_Deventer
Mixup Cube is like a Rubik's Cube, but with an unexpected twist. When a mid plane is turned by 45 degrees, other turns are possible. This way of turning mixes up the center and edge pieces. Although the concept has already been patented in 1985 by Sergey Makarov, this version has an internal 2x2x2 "cube" for extra stability.

Watch the YouTube video of version 1.
Watch the YouTube video of version 2.
Watch the YouTube video of version 3 (this).
Read more at the Twisty Puzzles Forum

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

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From: \$225.15

by Oskar_van_Deventer
Gear Shift is based on an idea by Bram Cohen. This puzzle has eight gears around a cube. All gears can turn together. But it is also possible to pull the gears apart in two sets of four. Each set of four can be turned individually. And there are three ways to split the gears. The object of this puzzle is similar to Rubik's Cube: scramble it and then try to solve it.

Read more at the Twisty Puzzles Forum

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

Or buy the mass-produced version of this puzzle is mefferts.com.

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From: \$129.61

by Magic
Truncated Sphere D11 with 3-fold symmetry.

This die is inspired by the repulsion force polyhedra. Nonetheless, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 11 points repulsing each others.

Actually, I calculated the positions of 11 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 2 poles (upper and lower face - parallel to the horizontal plane)
- 3 points around each pole
- 3 remaining points corresponding to 3 faces perpendicular to the horizontal plane

The result is a truncated sphere with 11 circular faces of same radius.

It is numbered from 1 to 11: 2 numbers are on faces (poles), 6 between vertices and face and  3 on edges. The sum of the numbers on the 3 upper vertices surronding the North pole is 18.  Same thing for the sum of the 3 numbers on the lower vertices surronding the South pole and the sum of the 3 numbers on the edges of the equator.

This die is made of a shell of 1.5mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth. They are quite big since they overlap the surrounding faces and thus should be very easy to read.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

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From: \$8.89

by Oskar_van_Deventer
Unlucky Twist is a 1x2x13 twisty puzzle, related to the Rubik's Cube. It is a tribute to Ola Jansson, who found a telescopic mechanism to create extremely long twisty puzzles, including his own 1x2x5 design.

Read more at the Twisty Puzzles Forum.

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

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From: \$131.48

by vertigopolka
This bauble is made of three nested truncated icosahedrons, or buckyballs.
Check out my other pendant models in my Jewelry/Pendant section.

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From: \$70.00

by Oskar_van_Deventer
Geared Mixup is a twisty-puzzle design requested by many people. When playing the original Gear Cube (Caution Cube), players can only make half turns because of the gears. Many people tried quarter turns in vain. Now it is possible, by combining the Gear Cube and Mixup Cube concepts. Geared Mixup has eight geared corners that drive twenty small 4-teeth gears.

Read more at the Twisty Puzzles Forum

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

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From: \$160.12

by Camazine
Successfully printed in stainless steel from a design courtesy of Bathsheba Grossman. The prices shown do not have any price markup since this model was provided gratis.

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From: \$4.18

by virtox
While playing on the math playground, I found this pretty pebble. Suitable as a pendant or bead.
Necklace not (yet) included, you will need a thin flexible cord to make the sharp turn on the inside.

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From: \$27.50

by virtox
A spiraling web cube

The cube contains 24 spirals intertwining.
A large, playful and decorative piece.

See video for full effect!

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From: \$37.50

by Oskar_van_Deventer
Fadi Cube is a twisty puzzle like Rubik's Cube. It is an attempt to use other than conventional slices to make a twisty puzzle. At first sight, it looks impossible to twist this puzzle at all. But the pieces go over and under each other to make it possible. According to Bram Cohen, the closest "relative" of Fadi Cube is Katsuhiko Okamoto's Lattice Cube.

Read more at the Twisty Puzzles Forum

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

Or buy the mass-produced Mosaic Cube version from Mefferts.

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From: \$326.59

by froland
Visually the complexity is puzzling.

See here for a larger version supporting more materials.

This first experiment yields an extremely flexible structure while maintaining a relativly high stability.

In the test print a few links broke, but the overall structure came out fine.
UPDATE: Modified to allow printability with new design rules.

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From: \$32.11

by virtox
Two separate but interpenetrating cubical gyroids.

Added color in images is to identify the two separate parts.
This is the monochrome version for one of the strong and flexible materials.
(so both parts will be the same color)

Alumide is experimental.

Full color version :
http://www.shapeways.com/model/107881/double_gyroid_color.html

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From: \$23.86

by Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the second, analogous to the octahedron, called the cross polytope.

The cross polytope is dual to the hypercube, so its 16 cells correspond to the 4-cube's 16 corners. This projection is a straightforward Schlegel diagram. A different projection is here.

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From: \$17.18

by henryseg
Produced using SeifertView (http://www.win.tue.nl/~vanwijk/seifertview/)

The figure 8 knot is the simplest knot after the trefoil and the unknot, and the simplest hyperbolic knot.

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From: \$20.88

by MindEversion
a formula based model.

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From: \$48.18

by virtox
A 3d printed stress toy.
So far it has turned out to be very resilient and helpful ;-)

(See video!) I recommend this for people in customer service, financial, development and executive departments ;-P

Shown is the old grey, currently available in White, Black, Red, Blue, Pink, and Purple!

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From: \$17.50

by opresco
• 12 faceted die (based on the dodecahedron) • Could be worn as a pendant • Lanyard not included
See my New Spring Loaded Dice:

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From: \$9.09

by SirisC
A d2 made from the dual of a standard sphereicon. (made from a cylinder instead of a dual-cone) Pips are placed on either side to see the result.

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From: \$5.08

by henryseg
A self-referential tessellation of the torus.

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From: \$21.69

by vertigopolka
A soccerball (truncated icosahedron) that has been layered, fractalized and softened a bit. (size: 3 inches)

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From: \$33.00

by virtox
This pair of loosely entangled bracelets is based on Gyroid bones.
A very elegant variation on the mathematical equation.
Width : 24mm / 0.9 Inch
Thickness : 9mm / 0.4 Inch
Size/Diameter : 40 - 70mm / 1.6 - 2.8 Inch

Each size is custom created for a uniform look and feel over all sizes.
It's quite flexible, so you can easily slide it over the hand.

If you would like a small opening in the bracelet so you can have a tighter fit, please leave a remark.

Slim version available here.

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From: \$15.00

by Oskar_van_Deventer
Jack's Cube was suggested by Jack via YouTube. The design was inspired on the Magic Sphere puzzle. Jack's Cube has three types of moves. First there are the conventional Rubik's turns. Secondly, a circle of nine pieces can turn in steps of 90 degrees. Finally, a great circle of 12 pieces can turn in steps of 30 degrees.

Read more at the Twisty Puzzles Forum.

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.

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From: \$248.63

by MindEversion
A spherical gyroid with voronoi structure.

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From: \$105.99

by unellenu
"Sphere within a sphere within a sphere" small sculpture with a moving ball within a ball (3 spheres in all). The surface consists of a structure formed from a voronoi pattern.

There is also a slightly larger 4 layered version available.

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

unellenu website unellenu.com

facebook: unellenu fractal sculpture & homewares

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From: \$45.00

by vertigopolka
A classic right-handed trefoil knot.
Check out additional models of knots and torus knots in my Knots section.
Also check out the pendant version: Trefoil Knot Pendant.

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From: \$5.00

by vertigopolka
Here's a very festive truncated icosahedron that knows how to party, or maybe partied just a little too much.

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From: \$21.00

by MindEversion
Interlocked Moebius in wireframe style
wall thickness is 1.6mm

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From: \$74.87

by Oskar_van_Deventer
Size 8, 18.54 mm inner diameter. This puzzle ring is a design by Bram Cohen. Bram writes: "It has basically a a single trick, but that trick is so cute and understandable that I think it's a compelling puzzle."

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From: \$13.40

by lelena70
author George Hart

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From: \$17.64

by arkonisus
Your cat will love it ... :-)

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From: \$17.22

by virtox
The hip bone connects to the gyroid bone ?
The gyroid bone, another wonder of nature and mathematics.
Tested in WSF, but I left all material options open for the daring.

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From: \$31.49

by swirlingbrain
I've attached a ball to the rolling ball sculpture with the idea that you cut it off and sand it and it should work as the marble. The marble is 5/8 inch so it should work with regular glass or wooden marbles too. Yea it works! See the video!

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From: \$11.42

by Bathsheba
The answer to the burning question, what would the sculpture Ora be like if it were a hypercube instead of a cube? A bigger one is here.

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From: \$12.21

by Magic
Double D6

This is a compound of a nearly regular D6 and of a sum-D6. As the sum-D6 that composes the shell gives results from 0 to 5, the core is numbered from 2 to 7.
As a consequence, when you roll this double die, you got the same results as summing the results of two regular D6. But in a very original way!
For instance, in the rendering, the upper face of the core show 3 pips and the upper part of the shell, around this face, shows 2 extra pips. Thus, the result is 3+1+1 that is 5.

SUCESSFULLY PRINTED in White Strong and Flexible.
Not printable in Metal, sorry (movable parts).

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From: \$9.99

by Magic
Double Coin D4
This is a D4 working as two interlocked coins.
Clearances are 0.5 mm and works perfectly for Strong and Flexible.

Also check the Double D6 based on a similar concept.

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From: \$21.90

by friz
The complete set of Catalan dice (except the triakistetrahedron, already available in various standalone versions) in four bundles. Hollow version. Note that the pentagonal icositetrahedron and the pentagonal hexecontahedron are not suitable as dice. I have added them for completeness.

Bundle 1.
Rhombic dodecahedron (12 faces)
Pentagonal icositetrahedron (24 faces)
Triakisoctahedron (24 faces)
Deltoidal hexecontahedron (60 faces)

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From: \$16.02