### Square Kaleidocycle

This book has many versions of kaliedocycles: cut out and glue to make many interesting mathematical objects.

From Amazon: **BUY NOW: MC Escher Kaleidocyles**

Square Kaleidocycle: a ring of eight linked tetrahedra. The hinged connections allow the ring to be rotated through its center. The faces of the pyramids are decorated with the famous tessellation work of MC Escher, a pattern of interlocking lizards. Note that as the kaleidocycle is rotated the lizards at the center change through each of four colors. Made from card stock, this kaleidocycle was cut and assembled from a book by mathematicians Doris Schattschneider and Wallace Walker.

### Pocket Scintillator Kinetic Art

Logan sometimes has items for sale here:

From Etsy: **BUY NOW: PocketScintillators**

Pocket Scintillator Card: three sheets of seemingly random arrays of translucent colored pixels produce words and images when stacked- shift the stack of sheets and a second images appears! Innovative kinetic optical art by inventor, artist, software developer Logan Kerby @thanksplease who kindly sent me these cards encoded with @physicsfun themes.

### In and Out Illusion

Similar objects available here- from Etsy:** BUY NOW**: ** Ambiguous Objects**

In or Out Illusion: this 3D printed sculpture incorporates the now famous Stubborn Arrow Illusion and features both a left and right handed version. These ambiguous object illusions are a fairly recent invention by mathematician Kokichi Sugihara of Meiji University in Japan which take advantage of a clever combination of perspective, and viewing angle.

### Ambiguous Object Illusion Set

This wonderful and afffordabe set includes four illusion objects and a mirror:

From curiositybox.com: **BUY NOW: Inq's Ambiguous Illusion Kit (sold out)**

Similar objects available here- from Etsy:** BUY NOW**: ** Ambiguous Objects**

Ambiguous Object Illusion Set: This kit comes with four objects (three shown here) invented by mathematician Kokichi Sugihara of Meiji University in Japan. Polygons appear as circles in a mirror and vice versa, and the famous “stubborn arrow” that will only point to the right (or, in a mirror, to the left). I like how the base is also an ambiguous pentagon/circle, which like all these objects, is a result of a clever combination of reflection, perspective, and viewing angle. Thanks to the Vsauce team for producing this kit!

### The Holoscope: Cube with Spheres

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

The Holoscope: a cube of mirrors with the interior viewed from one corner and illuminated by light entering from glass spheres at the other seven vertices. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### Beaded Kaleidocycle

Get similar beadwork geometric art here:

From Etsy: **BUY NOW: Beadwork Kaleidocycle**

Beaded Kaleidocycle: based on a geometry of six linked tetrahedra with hinged connections that allow the ring to be rotated through its center. Intricate beadwork meets math in this kinetic artwork by Erin Peña.

### The Holoscope : Icosahedron

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

Look through other holoscopes in my collection here: Holoscope Kaleidoscopes

The Holoscope Icosahedron: the intricate beauty of multiple internal reflections from 20 triangular mirrors in the shape of this famous platonic solid. The interior is viewed from one corner and illuminated by light entering from glass spheres placed at all of the other 11 vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison, (swipe to see the dodecahedron and cube) and future posts will include tetrahedron and octahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### Sphere Sticks Geometric Puzzle

Get this affordable and amazing puzzle here:

From Etsy: **BUY NOW: Sphere Sticks**

Sphere Sticks Puzzle: 30 identical wood pieces, each with two notches as shown, can create 12 interlocking pentagons in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 4 others that connect with it. Precision cut notches on the rods allow them to interlock with elastic tension such that vector sum of the 4 forces sum to zero in this tensegrity type equilibrium. The dodecahedron, with its 30 edges and 12 sides, is the basis of this puzzle sculpture.

### The DeltaCELT Rattleback

Get one here:

From Etsy: **BUY NOW: The DeltaCELT**

The DeltaCELT: a new rattleback design where the indentations create an asymmetry in the distribution of mass that leads to rotation reversals when spun: 1) If spun clockwise, after about two full rotations, a complicated combination of friction, precession, and instability induced vibrations transforms the rotational energy into into end-to-end rattling (energy of oscillations) and then into rotational energy in the opposite direction. 2) If spun counter-clockwise, after about 30 full rotations the rotational energy translates into side-to-side oscillations leading to a clockwise reversal (swipe to see- less dramatic but still amazing). The design is made of solid brass and has the shape of a bisected prolate ellipsoid in the proportion of the mathematical constant δ =4.669.. (Feigenbaum dynamical constant) giving the name to this new design by astrophysicist Kenneth Brecher. The DeltaCELT comes with the polished slate spinning surface for optimal performance.

### High Voltage Fractal in Wood

Amazing creations made here:

From Etsy store EngravedGrain:** BUY NOW High Voltage Fractal **

High Voltage Fractal in Wood: a Lichtenberg fractal created by a high voltage electrical current flow across a piece of wood. Since wood is an insulator a light coating of conducting water (for instance a solution of baking soda or salt) is first applied to the surface. Metal electrodes are then attached at each end of the wood piece and a dangerous source of high voltage is applied (such as a microwave oven transformer or neon light transformer).

### Dandelin Spheres

I found this beautiful model on eBay and I'm not sure of its age or origin.

Grant Sanderson describes the elegant geometry behind this curious arrangement.

On YouTube: **3Blue1Brown descibes the Dandelin Spheres**

Wikipedia also has a good description: **the Dandelin Spheres**

See how sliced cones create conic sections with these colorful foam versions:

From Ammazon: **BUY NOW: Conic Sections**

Dandelin Spheres: Slicing a cone with a plane can produce an ellipse, and two spheres encapsulated by the same cone will always have the small sphere touching one focus and the large sphere contacting the plane at the other focus. This beautiful acrylic model shows this geometry for one choice of cone width and dissecting plane angle- but it always true. This geometric construction is named for its inventor, French mathematician Germinal Pierre Dandelin back in 1822, and with it he proved theorems concerning properties of ellipses and other conic sections- mathematical entities that play a roll in much physics- including the orbits of planets. Fun math that I wish someone would have showed me back in high school!

### Ambiguous Object

These type of objects were invented by mathematician Kokichi Sugihara, and you can buy his other books here:

From Amazon:** BUY NOW Ambiguous Objects by Kokichi Sugihara **

Also available from Amazon (Japan):** BUY NOW set of four ambiguous objects with booklet **

Similar objects available here- from Etsy:** BUY NOW**: ** Ambiguous Objects**

Another illusion design by Kokichi Sugihara of Meiji University in Japan, the inventor of this illusion and art form. A mathematically calculated combination of perspective and the physics of reflection produce this striking illusion that works in many configurations.

### Holoscopes: Dodecahedron and Cube

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

Look through other holoscopes in my collection here: Holoscope Kaleidoscopes

Holoscopes: polyhedra of mirrors (dodecahedron and cube) with the interior viewed from one corner and illuminated by light entering from glass spheres placed at all of the other vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison @holoscope2000, and future posts will include tetrahedron, octahedron, and icosahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### The Klein Bottle

The best Klein Bottles are made by Cliff Stoll, astronomer, mathematician and artist. Every one-sided, zero volume bottle is packaged and shipped by Cliff himself. Get one today!

From ACME Klein Bottles: **Buy NOW Klein Bottles by Cliff Stoll **

Wikipedia has great details on the Klien Bottle, and the amazing Cliff Stoll.

The Klein Bottle: 3D representation of a four dimensional mathematical object with one side, no edges, and zero volume. Kind of like a Möbius strip with no edges.* Math meets glass art! Many thanks to Cliff Stoll for this kind gift and a great visit including a wonderful tour of his collection of mathematical oddities. *only achievable in 4D.

### Dudeney's Dissection

A nice wood version is available here:

From Etsy: **BUY NOW Dudeney's Dissection **

Click here for** other intresting versions of this puzzle**

See both Wikipedia and Wolfram MathWorld for more details on the history and math of this geometrical oddity.

Dudeney's Dissection: an equilateral triangle can be cut (dissected) into four pieces that will then assemble into a square. Interestingly the four parts are all different in shape (the green and yellow pieces are similar but not the same). This hinged model is comprised of precision machined and anodized aluminum, and can be folded back and forth between the two simplest regular polygons. It is not known if a similar three piece dissection is possible. Also called the haberdasher's problem and described in 1907 by Henry Dudeney it is the only 4 piece solution known.

### Infinity Cube Sculpture

Get an infinity cube here (many colors and sizes to choose from):

From Ricardo Churchill (Etsy): **BUY NOW: Infinity Cube**

Infinity Cube Sculpture: crafted from solid stainless steel and powder coated orange, the geometry of this mathematical sculpture is the perimeter of the faces of a cube traced by a nonintersecting connection of equal line segments. When viewed from a corner, a cube has a hexagonal cross section, and some may recall the famous logo of Silicon Graphics computers based on such an infinity cube (a design by Scott Kim). Rotating this “tubed cube” along a diagonal axis reveals the interesting symmetries of this geometric construction.

### 3-Shuttle Trammel of Archimedes

Get this device here:

**BUY NOW: 3 shuttle device**

This device came in my Curiosity Box subscrition. A great way to start collecting your own physics toys (and other brain food):

From the Vsauce team: **BUY NOW: The Curiosity Box (New box will ship soon- get a great deal now)**

Get similar (two shuttle) devices here:

From Etsy:** BUY NOW **

Trammel of Archimedes

3-Shuttle Trammel of Archimedes: as the shuttles take turns completing their straight line journeys, the end of the crank arm traces an ellipse. This precision 3-shuttle version by the VSauce team came in my @thecuriositybox - made with high quality molded plastic parts that produce very smooth movement- a wonderful addition to my collection! Sometimes sold as a “do nothing machine” or “nothing grinder”, far from doing nothing this simple and crucially important mechanism demonstrates how rotational motion can be converted into translational oscillatory motion- such as how a piston can drive an engine’s crankshaft.

### Platonic Solids Dice Set

Get this nice set of regular polyhedra dice here:

From Etsy: **BUY NOW: Polyhedra Dice Set**

Less expensive sets of standard plastic dice here:

From Amazon: **BUY NOW: Polyhedra Dice Set**

Platonic Solids Dice Set: The five famous convex regular polyhedra in the form of fair dice. This set is cast in metal with clean edges and makes for a great way to own these symmetrical objects that have fascinated thinkers ever since the ancient Greeks wrote about them circa 360 BC. Only these five forms meet these criteria (in 3D space) for each face: must be equal in size, be equal in number of sides, each side of equal length, identical in angle were any two sides meet, and have the same number of sides meet at each vertex point of the solid. 2000 years later the famous mathematician Euler determined that for these 5 shapes V-E+F=2, the number of corners (vertices), minus the number of edges, plus the number of faces, will always equal 2.