### 10 Hex Puzzle

This and other beautiful and well made puzzles are available on Etsy:

From Etsy: **BUY NOW 10 Hex Puzzle **

Two great resources about these polyhexs: polyform puzzler page and puzzleworld page

10 Hex Puzzle: this puzzle is comprised of pieces which are the set of all ways three and four hexagons can be joined with a common edge. There are 3 trihexs and 7 possible tetrahexs, and similar to pentominoes, these 10 polyhexs can assemble into a large hexagon. Amazingly there are exactly 12,290 solutions to this puzzle- but it’s still a challenge to find just one!

### Hexa Sphericon

Sphericon and Hexa-sphericon: order your set today!

From the Matter Collection:** BUY NOW The Sphericon (Hex and Regular) **

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane. Solids from the sphericon family all have one side and two edges. Each sphericon is based on a regular polygon, with the basic sphericon derived from a square, and here- a more interesting case with more complex rolling motion- from a hexagon.

### Vsauce Mirror Anamorphosis

Currently this mirror and image set comes to you (in the Summer 2020 box) with any subscription:

From the Vsauce team: **BUY NOW: The Curiosity Box**

The Curiosity Box is an excellent way to start your own physics toy collection- reccomended highly!

For those who want to see the math behind this art, here is an initial paper on the topic published in 2000 in the American Journal of Physics: Anamorphic Images by Hunt et al.

Vsauce Mirror Anamorphosis: the warped printed image is restored only with a mirror in the form of cylinder- when placed carefully in the center of the image, Kevin, Michael, and Jake appear in their true form. This mirror (along with a set of images and DIY templates) came to me last week in the most recent @thecuriositybox- a fantastic way to start your own physics toy collection. The math describing this anamorphic mapping is quite complex and is nicely detailed in a physics journal article from 2000.

### Pentominoes

Get this set here:

From Etsy: **BUY NOW Hardwood Pentominoes **

Many versions available here:

From Amazon:** BUY NOW Pentominoes **

The book by mathematician Solomon Golomb that started the polyonomo recreational math craze:

From Amazon: **BUY NOW: Polyominoes **

Pentominoes: The 12 possible arrangements of five identical squares joined edge to edge. Since 5x12=60, the pentominoes can tile a 6 x 10 rectangle with no gaps (2339 ways to do this- yet even finding one solution is a challenge). I love this beautiful set from artist/woodworker Ron Moore where each pentomino is made from a different kind of hard wood.

### The *e*TOP

Get this and other beautifully crafted math themed tops here:

Fropm Etsy: **BUY NOW: The ***e*TOP

The eTOP: an ellipsoid based on the famous Euler’s constant e, diameter 2” and thickness 2/e”- spinning magnets from the magnetic stirrer induce electric currents to flow in the copper eTOP- these currents then create their own magnetic field which opposes the magnets underneath and pushes the eTOP to spin, producing interesting motion and sound. Credit to astrophysicist Kenneth Brecher, the creator of the eTOP, PhiTOP, and this unique means of using Lenz’s Law to spin it up. This top stands up vertically (when spun with sufficient rotational velocity) due to physics similar to that of the tippe-top. The concave mirror keeps the top from wandering off of magnetic stirrer.

### Novascope Kaleidoscope

The Novascope can be ordered from the artist here:

From novascopes.com: **Order here Novascope by David Sugich **

Novascopes can sometimes be found on eBay

From eBay:** Search NOW Novascope Kaleidoscopes **

Novascope: tapered mirror kaleidoscope by David Sugich uses three mirrors to create an image of geodesic spheres. Three mirrors in an equilateral triangle configuration will produce a plane of tiled triangles, but if they are tapered the repeated reflections curve to infinity creating the spherical geometry. In this design there are thin gaps etched into one mirror which allows in colored light from a flashlight (on the white side of the pyramid shaped scope) to produce the hexagon lattice. Shining a light through the view portal reveals where the colored lines come from as a flashlight moves from top to bottom and back. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.

### Mirror Anamorphosis

This image by István Orosz is available as a poster and as a puzzle:

From Amazon:** BUY NOW Mysterious Island Puzzle **

From MathArtFun.com:** BUY NOW Mysterious Island Poster **

For those who want to see the math behind this art, here is an initial paper on the topic published in 2000 in the American Journal of Physics: Anamorphic Images by Hunt et al.

Many books are available (with mirror cylinders) from Amazon: Anamorphic Art in Books

Mirror Anamorphosis: this famous print by artist István Orosz has a hidden anamorphic image revealed by placing a mirrored cylinder over the depiction of the moon in the image. The work visualizes a scene from the book “The Mysterious Island” by the science-fiction author Jules Verne- whose portrait emerges in the reflection on the cylinder. The math describing this mapping is quite complex and was given in detail in a physics journal in 2000, but before that Martin Gardner described the math in 1975. Repost for this week’s theme as I head to G4G!

### Shadow Stereographic Projection

These mathematical art objects are created by Henry Segerman and available here:

From Shapeways:** BUY NOW Mathematical Art **

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 a square grid, and a honeycomb of regular hexagons. 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.

### Equilateral Triangular Kaleidoscope

This inexpansive kaleidoscope is available here:

From increadiblescience: **BUY NOW: Moire Tube Kaleidoscope**

Click here for affordable, precision made scopes with angled mirrors: **Kaleidoscope Symmetries Explored**

See more kaleidoscopes in my collection: Kaleidoscopes

Equilateral Triangular Kaleidoscope: three mirrors arranged in a 60-60-60 degree triangle creates the appearance of a plane filled with triangles (or equivalently a honeycomb lattice)- perhaps the most common mirror configuration design, this inexpensive kaleidoscope produces an excellent example of the reflection pattern. As a bonus the exterior tube on this scope incorporates a kinetic Moirè pattern. The kaleidoscope was invented by the famous Scottish physicist Sir David Brewster (1781-1868), and has become an entire field of artistic endeavor.

### Oloids: Solid and Anit-oloid

Order your Anti-Oliod today: available in three types of metal:

From The Matter Collection: **ORDER NOW: Anti-Oloids in Brass, Copper, and Steel **

Oloids: “solid hull” and “ruled surface” types made from brass and copper- oloids are unique solids that roll in such a way that every point on their surface comes in contact with the plane. The basis of the oliod’s geometry is that of two connected circles, one perpendicular to the other such that the rim of each circle goes through the center of the other. The shapes you see here are the results of connecting the rims of these circles together with a family of straight lines, one method leads to the solid convex hull form, and another way leads to the ruled oloid (anti-oloid).

### Tapered Mirrors Kaleidoscope

This design by Koji Yamami available here:

From kaleidoscopeshop.com: **BUY NOW Space Teleiedoscope **

Click on this link for details on the physics and symmetries of two mirror kaleidoscopes.

Tapered Mirrors Kaleidoscope: the unique design of this teleidoscope uses three mirrors to create an image of a geodesic sphere. As can be seen through the semi-transparent acrylic tube, the three mirrors are tapered, with their smaller ends near the ball shaped lens. Three mirrors in an equilateral triangle configuration will produce a plane of tiled triangles, but if they are tapered the repeated reflections curve to infinity creating the sphere. In this design by Koji Yamami there are small gaps between the mirrors which allows in colored light from the iridescent tube to produce the radiant streaks of light. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.

### 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.