### Opticum 3 Font

Get your custom message engraved here:

From Creative Crafthouse on Etsy: **BUY NOW Custom Opticum Font Message Plaque **

This family of fonts is available here: Opticum 3 from Linotype

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Opticum 3 Font: This laser engraved message uses the Opticum 3 font designed by Erken Kagarov, where indirect lighting reveals the symbols hidden in a maze- created by simply typing out your message using this font. Amazing application of geometry and shadow!

### Inverting Valentines Illusion

This 3D printed illusion available here:

From Shapeways:** BUY NOW Red Hearts Illusion Object **

Similar item here:

From Etsy: **BUY NOW: Red Hearts Illusion**

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Inverting Valentines Illusion: Love is a matter of perspective in this illusion that depends on viewing angle. A sweet take on the ambiguous object illusion invented by Kokichi Sugihara of Meiji University.

### Rhombic Blocks Mathematical Puzzle

This beautifully made puzzle available here::

From Etsy: **BUY NOW Rhombic Blocks **

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Rhombic Blocks Mathematical Puzzle: There are 9 possible ways three rhombuses can be joined together along a common edge, and similar to pentominoes, these 9 tri-rhombs can tile a polyhedron, in this case a hexagon. There are 14 solutions to this puzzle, and one where no same-colored pieces touch. A beautiful math discovery by puzzle master Stuart Coffin.

### High Voltage Fractal in Wood

Amazing creations made here:

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

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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).

### Logarithmic Spiral Gears

Amazing kinetitc creations made here:

From Etsy:** BUY NOW: Spiral Gear Set 3D Printed**

Original 3D print files available here:

From Thingverse:** Spiral Gear Set **

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Logarithmic 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 laser cut based on 3D prints of Misha Tikh and the research of Balint et al.

### Holoscopes

Order a holoscope from the artist's gallery here:

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

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6 and 12 Faced Holoscopes: a cube and dodecahedron of mirrors. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison @holoscope2000. These holoscopes are in the form of two famous Platonic solids- each with all the corners cut off to allow light to enter through triangular holes. Through the symmetry of the reflections, these triangles appear as an infinite array of tetrahedron shapes in the dodecahedron, and as beautiful repeating stellated octahedrons in the cube. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### Skew Dice

Available here!

From Amazon: **BUY NOW Skew Dice**

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Skew Dice: 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 are a special type of polyhedra called asymmetric trigonal trapezohedra which come in right and left handed versions- this set has one of each (mirror images of each other). What allows this shape to be fair like a cube has to do with the 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.

### Orbiforms

Orbiforms available here:

From Etsy: **BUY NOW Orbiforms**

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Orbiforms: volumes of constant width made from solid steel, brass, and copper- these shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate stays parallel to the table as the orbiforms roll underneath. The first set shown are based on the Reuleaux triangle and the second set are based on a Reuleaux pentagon. Featured items from @altdynamic** **

### The Galton Board

Available here:

From Amazon: **BUY NOW Galton Board **

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The Galton Board: 3000 steel balls fall through 12 levels of branching paths and always end up matching a bell curve distribution. Each ball has a 50/50 chance of following each branch such that the balls are distributed at the bottom by the mathematical binomial distribution. One of my favorite finds of 2018! An elegantly designed modern version of the Galton Box invented by Sir Francis Galton(1894) to demonstrate the Central Limit Theorem - showing how random processes gather around the mean. In addition the number of balls in each bin can be predicted by Pascal's triangle (printed on the face over the pegs).

### Tension Integrity Icosohedron: Tensegrity

Get this kit and build one:

From Etsy: **BUY NOW: Tensegrity Kit**

A nice version of this tensegrity icosohedron is sold as a toy for tiny tots:

From Amazon:** BUY NOW Tensegrity Toy **

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I constructed this version by referring to the images and descriptions of tensegity on Wikipedia

Tension Integrity Icosohedron: Six brass struts float isolated from each other but held in a stable configuration by a net of 24 connecting cables. I made this sculpture using hollow brass tubes and weaving through them a single strand of fishing line, which is connected after passing through each tube exactly four times. This configuration of three sets of parallel struts forms a Jessen’s icosahedron under tension, and was invented by the famous architect Buckminster Fuller in 1949.

### Impossible Card Case

Get this fun card case here and support this amazing museum:

From the MoMath Store: **BUY NOW: Rollover Card Case**

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Impossible Card Case: this business card carrier has a special double hinge that allows it to be opened from either side, and transforms from stripes of white and silver to black and silver. I use this to carry @physicsfun bling diffractive stickers. Sometimes called a magic or flip case, the ribbon construction is similar to the famous Jacob’s Ladder toy I’ve featured and dscribed.

### Hyperbolic Holes

This inexpensive kit available here:

From Amazon: ** BUY NOW: Hyperbolic Holes Kit**

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Hyperbolic Holes: a straight rod, in this case a pencil, glides through a symmetrical pair of curved holes. The design is based on the hyperboloid, the 3D ruled surface traced by an offset rotating diagonal line. This device is sold as an inexpensive kit to assemble yourself, and includes a motor with geared drive and pre-cut pieces. The pencil is my addition- sharpened to just the right size to clear the curved openings.

### Klein Bottle

Get this mathematical glass art here:

From Etsy: **BUY NOW: Klein Bottle**

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Wikipedia has great details on the Klein Bottle

Klein Bottle: 3D representation of a four dimensional mathematical object with one side, no edges, and zero volume. Kind of like a MoĢbius strip with no edges.* Math meets glass art with this fun “lamp shaped” version! *only achievable in 4D space

Speed cube version available here:

From Amazon; **BUY NOW: 1x1x1 cube**

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Completing the collection: the 1x1x1 cube, a silly but logical addition to any twisty cube collection!

### Jack in the Box Puzzle

Order this amazing puzzle here:

From Craighill & Art of Play: **Order Now: Jack in the Box**

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Jack in the Box Puzzle: eight solid aluminum pieces form a textured cube when carefully stacked- yet the same eight pieces can also be packed around a six pronged “jack” to form a second smooth silver cube that is barely larger that the first. Similar to the 2D Matsuyama’s paradox puzzle, a small square is centered on each face of the cube in the second solution. Some stages of assembly shown here under rotation to emphasize the beautiful symmetries in the design and avoid spoilers to the challenge. Created by Rod Bogart and engineered into existence by the talented folks at @craighillcompany, and I send a hearty thank you to my friends at @artofplay for sending me this unique and special puzzle.

### The Magic Octagon Coin

Get this new amazing coin here:

From Shire Post Mint: **BUY NOW: Magic Octagon Coin**

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“Magic Octagon” Challenge: introducing a beautiful copper coin version of this puzzle of successive rotations. Which way will the light arrow point after left and right rotations of the dark arrow? No trickery here- just the math of geometry, symmetry, rotations, and reflections and how our intuitions often fail us upon first attempts. Swipe twice for second challenge. In collaboration with my friends at @shirepostmint

### Square Dissection Puzzles

Get these and other well made disection puzzles here:

From Etsy: **BUY NOW: Square Dissection Puzzles**

These puzzles are expertly laser cut and sold by GamesEfce. I spray-painted the pieces of mine to better show the shapes and relationships for the video.

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Square Dissection Puzzles: a square can be cut (dissected) into polygons and then reassembled into other regular polygons. Shown here: an equilateral triangle, a pentagon, and a hexagon. These are the record holders for smallest number of pieces needed: triangle (4 pieces by Henry Dudeney 1902), hexagon (5 pieces Paul Busschop 1870s) and pentagon (6 pieces Robert Brodie 1891). Fun fact- It is not known if any of these records are the smallest possible, no mathematical proofs yet exist on this question.

### Puzzle in a Puzzle: Extra Square

Get this and other amazing math puzzles here:

From Etsy: **BUY NOW: Extra Square Puzzle**

See also**: **Matsuyama's Paradox

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Puzzle in a Puzzle: 12 pieces fill both large square areas- but the bottom has 5 tiny squares in its center compared to 4 in the top. All 9 tiny squares are identical in size, and the large square areas are also identical. So where did the extra square go? Some fun math involved in the design of this puzzle, which illustrates how the concept of area can challenge our intuitions. Another precision crafted puzzle by Jeux Efcé game shop.