Math Toys

Countdown Dice

Get a set here:

From The Dice Lab: BUY NOW: Countdown Dice

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Countdown Dice: roll these d24 dice carefully and the number on the top surface will count up or count down in sequence! The geometric form that allows this behavior is called a sphericon, a convex solid discovered by David Hirsch that has the properties of a developable roller, a shape where every part of its surface makes contact with the plane on which it rolls. Another unique and interesting die design by Henry Segerman and The Dice Lab.

Nautilus Spiral Gears

Get this inexpensive 3D printed set here:

From Etsy: BUY NOW: Nautilus Gear Set

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Nautilus Spiral Gears: an extreme example of non-circular gear sets. This set is based on the famous Fibonacci spiral and evokes the cross section of nautilus shell with internal chambers. If one gear of this set is turned at constant speed, the other will turn with an varying speed. A 3D print of Misha Tikh and the research of Balint et al. 

Rolling Uphill Illusion

Availabel here:
From Etsy: BUY NOW: Uphill Ramp Illusion

or get the 3D print file here:
From Thingverse: Download Now: Uphill Illusion

Learn more: The amazing illusions of Kokichi Sugihara
See the many other Sugihara Illusions: in my collection

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Rolling Uphill Illusion: the ball bearings seemingly roll uphill as if attracted by magnets of some kind. What’s going on? Swipe for reveal as it is truly a matter of perspective. A wonderful take on an illusion invented by Kokichi Sugihara of Meiji University. 3D printed by my good friend @zathras5 (Roger Key) from a file designed by Julian Hardy. 

Shadow Stereographic Projection

These mathematical art objects are created by Henry Segerman and are available here: 
From Shapeways: BUY NOW Mathematical Art 

US Flag projection can be obtain here (Support MoMATH!);
From MoMATH: BUY NOW: US Flag Stereo Projection

Note: this site contains affiliate links for which I may be compensated

Wikipedia has a nice introduction to the math and applications of stereographic projection

Shadow Stereographic Projection: 3D printed sculptures that cast geometric shadows. When illuminated by a point source of light (placed at the top pole of the sphere) the shadow cast by the rays of light represent a one to one mapping of the points on the sphere to points on the plane- creating 1) the US Flag, 2) a honeycomb of regular hexagons, and 3) a square grid. Stereographic projection is often used in representing the geography of the globe of our planet on to a flat map. Mathematical art by Henry Segerman.

Wireframe Ambiguous Cube

Get the files (or order one printed) here:
From MakeAnything's MyMiniFactory: BUY NOW: Illusion Cube 3D Print Files
From Shapeways: BUY NOW: Ambiguous Cube Illusion

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See the other illusions my collection: Ambiguous Objects

Wireframe Ambiguous Cube: another innovation of the ambiguous object illusion invented by mathematician Kokichi Sugihara of Meiji University- this time a 3D frame of a cube transforms to a cylinder! A new 3D print design from @make.anything

Tapered 4-Mirror Kaleidoscope

These precision kaleidoscopes are crafted from front surface mirrors and other specialty materials, many with innovative design and construction techniques:

From Etsy: BUY NOW: Kaleidoscopes by Marc Tickle

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Tapered 4-Mirror Kaleidoscope: not CGI- these images are produced by mirrors and light! Hidden within this colorful tube are 4 mirrors, 2 rolling glass spheres, and 1 dichroic glass reflector. These elements combine to produce the dynamic and magical images seen through the view window as the device is slightly tilted back and forth and brought in and out of a bright light source. Entitled “Dichroic Disco” this piece is but one of many amazing creations by artist Marc Tickle, taking kaleidoscope design to the next level. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.

Interactive Logic Gate Display

Get this device here:

From Etsy: BUY NOW: Interactive Logic Gate Display

Note: this site contains affiliate links for which I may be compensated

Interactive Logic Gate Display: the most basic four binary/Boolean logic operations that are the fundamental components of modern computers- presented here appropriately on a standard green printed circuit board (PCB) complete with the truth table for each device. These logic gates are the basic building blocks of any logic circuit, from multiplexers, arithmetic logic units, and computer memory to full microprocessors which may contain hundreds of millions of such gates on a microchip. An educational, elegant, and fun design by Tyler Jacobs. 

Skew Dice (d6 and d12)

Get these skew dice here:

From Amazon: BUY NOW: Skew d6 set
From Amazon: BUY NOW: Skew d12 set

Click here for other amazing dice.

Note: this site contains affiliate links for which I may be compensated

Skew Dice (d6 and d12): these dice are skewed- but their odds aren’t! These unusually shaped dice are completely fair- roll them and the probability of outcomes are identical to a standard set of dice. The odd shapes of the skew d6s are a special type of polyhedra called asymmetric trigonal trapezohedra, and these d12s are tetrahedic pentagon dodecahedrons (swipe). These skew forms come in right and left handed versions(swipe twice) and these sets come with one of each mirror image. What allows these shapes to be fair like a cube has to do with their property of being isohedral, where each face of an object will map onto all other faces via a symmetry of the object. Manufactured by The Dice Lab team of Robert Fathauer and Henry Segerman.

Tesseract Projection

Get this CNC machined math art here: 

From AltDynamic: BUYNOW: Hypercube/Tesseract

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Tesseract Projection: a shadow of the 4-dimensional analogue to the cube, also called a hypercube or 8-cell. A tesseract(4D) is to a cube(3D) as a cube is to a square(2D). This piece of mathematical art is CNC machined from a solid piece of aluminum and anodized black- a representation, including perspective, of one possible shadow a hypercube could cast into 3D space. Multidimensional mathematics are often used in the formulations of physics, and visualizations such as this one help give insights. Another amazing creation from @altdynamic design studio.

CMY Platonic Solids

Available from these sources:
From CMY Cubes: All 5 Platonic Solids
From Amazon: BUY NOW: CMY Cubes and More

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Check out this nice set of Platonic Solids gaming dice

CMY Platonic Solids: The five famous convex regular polyhedra with thin film coatings, Cyan, Magenta, and Yellow, that allow filtering of the light that enters or leaves particular facets of each acrylic prism. I was struck by the intricate patterns produced in each object’s shadow by the refracted light- especially as the objects rotate. 

CUMOS Cube Kaleidoscope

The CUMOS Cube is a creation of artist Minori Yamazaki. Available for purchase- inquire via the contact info below:

From Etsy: BUY NOW: Cosmos in a Box

Fron Art of Play: BUY NOW:  Cosmos in a Box

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CUMOS Cube: a variation on the Kaleidoscope by artist @minori.yamazaki that produces a Cosmos in a box. So much wonder hidden within this unassuming white cube where etchings on front surface mirrors produce the repeating geometric patterns. A moving light source (led flashlight) is projected on the cube producing the dazzling animation effect on the multiple reflections. 

Dodecahedron Infinity Mirror

This lamp is interesting, but the fabrication is low quality. Still, it is fun to see the internal reflections and it would make for a great party light. Definitely read the reviews before purchasing! ($30-$45 USD) 

From Amazon: Dodecahedron Infinty Lamp

Note: this site contains affiliate links for which I may be compensated

Dodecahedron Infinity Lamp: lit from within by strips of LEDs the 12 plastic mirrored faces create a universe of interesting internal reflections. While the manufacturing quality of this item is pretty low, when the lights are off it looks pretty amazing.


Wobbler Roller

Get this very nice laser cut version here:

From Etsy: BUY NOW: Desk Wobbler

Note: this site contains affiliate links for which I may be compensated

Check out my posts on similar geometric objects: developable rollers

Wobbler Roller: a very simple toy today- two half circle perimeters affixed at right angles which surprisingly can then roll in a straight line with a peculiar wobble motion. When rolling, a wobbler always touches the table top at two points which could be connected by a straight line, and forms the frame of the geometric shape called a sphericon (featured in a previous post). 

Dymaxion Map

Get one there:

From Art of Play: BUY NOW: Dymaxion Folding Globe

Note: this site contains affiliate links for which I may be compensated

Dymaxion Map: today some math fun with this unique mapping of the Earth where the globe is projected onto an icosahedron and then unfolded onto two dimensions. Invented by the famous architect R. Buckminster Fuller, the Dymaxion projection map is designed such that it does not have a “right way up” and showing the continents as “one island Earth”. This mapping also produces less distortion of relative areas and shapes- note here that Greenland looks, correctly, much smaller than Africa- unlike what is seen on many world maps where they look the same size. This version, designed by Brendan Ravenhill, uses flat magnets to allow a very satisfying transformation between the flat 2D net and the 3D icosahedron “globe”.

Soma and Rhoma Puzzles

The Rhoma Cube is a vintage item and can sometimes be found on Etsy

Soma Cubes are available in wide viariety: 

From Amazon: BUY NOW: Soma Cube

From Etsy: BUY NOW: Rhoma Puzzle

Note: this site contains affiliate links for which I may be compensated

SOMA and RHOMA Puzzles: Replace every cube in the Soma puzzle with a rhombohedron to create the Rhoma puzzle- where the seven slanted pieces now make a larger rhombohedron. Here I’ve painted the corresponding Soma and Rhoma pieces to match on these sister puzzles that share identical edge lengths. While there are 240 ways to make the larger cube from the 7 Soma pieces, there is only one solution for the 7 Rhoma pieces. The original Soma Cube is a math toy has an interesting connection to physics- invented by Danish scientist and artist Piet Hein who claimed that this puzzle idea came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg in 1933. The seven pieces are all the ways 3 or 4 cubes can be joined, such that each piece has at least one inside corner.