Awesome Geometry

A Möbius strip is a twisted object that loops back onto itself, so it has only a single side. Brandon from Inheritance Machining shows us how he made a similarly perplexing object out of a single block of steel. Like the strip, his Möbius cube has one continuous side, but it was far more complicated to engineer and craft than its source of inspiration.

Greg Blanpied makes CNC-machined and laser-cut functional art fabricated using parametric math and geometry. Among his amazing pieces is this elegant bowl, which acts as a zoetrope when filmed or spun beneath a strobe light. He’s also created a zoetrope vase.

AltDynamic is back with two larger sizes of its Superegg desk plaything. The machined metal eggs feature a superelliptical shape, and now come in 2.4″ (Mighty) and 2.88″ (Mega) variants. Each can be ordered in stainless steel, copper, or titanium, with mirror, satin, or machined finishes. Mini and Classic sizes are also available during this Kickstarter campaign.

This set of geared shapes works like a Spirograph but lets you create more complicated and diverse patterns. The Planarc 2.0 Spiral Maker set includes 10 gears, three rings, and an outer frame to help you draw countless geometric designs. The basic set is made from acrylic, but there’s an aluminum version for a little more money.

Object manipulator SHAO shows off an amazing stage prop that can smoothly change shapes in the hands of the right performer. Designed by flow arts prop maker Thomas Foyk, this series of interconnected rods can morph from a cube into various other geometries.

Mathematician and maker Henry Segerman shows off more of his fascinating interactive mechanisms. This series of interlocking straight gears uses a rack-and-pinion mechanism to transmit motion. Henry posted the models to 3D print your own recursive racks on Printables.

This duo of stainless steel tools helps with measuring, drawing, and other everyday tasks. The wallet-friendly Horizon Helvetica features inch, cm, pixel, and pica rulers, a compass, a protractor, a t-square, a set square, and an isometric grid. Its sibling, the Horizon Key, has a bottle opener, hex bolt wrenches, a mini saw, a spoke wrench, a screwdriver, and more.

There’s a good reason that wheels are round: friction. But basic physics are never going to stand in the way of mad builder The Q. His latest creation is a standard bike frame with one major modification – it rolls on custom-made square wheels. It rides pretty smoothly, but it also doesn’t work how we assumed it would.

Most of us are familiar with pentagons, hexagons, and octagons, but did you know there’s a name for a 1000-sided shape? Thanks to its numerous vertices, the chiliagon looks like a circle to the naked eye and only reveals its true nature when viewed close up. Micheal from Vsauce offers a quick take on this unusual shape.

We’ve been spellbound by the many unconventional LEGO structures posted on the Brick Bending channel. For this creation, they linked together 3696 1×2 plates with 72 2×2 plates to create a spherical rhombicuboctahedron. You’d never know where this build was going if we didn’t tell you first.

Penrose tiles are a kind of arrangement in which polygons create patterns that never repeat. Minutephysics teamed up with Aatish Bhatia to explain the grid that underlies Penrose tiles and the math and geometry that prevents repetition. You can play with Penrose and similar patterns on Bhatia’s Pattern Collider.

Rapidly spinning objects can result in some cool, Spirograph-like patterns. LEGO mechanical builder Yoshihito Isogawa shows how different arrangements of LEGO Technic gears create different geometric patterns when spun in front of a camera’s lens. It would be interesting to see some larger and more complicated designs.

A while back, Stuff Made Here showed off an early version of his robot that could solve simple jigsaw puzzles. After refining the robot’s hardware and rewriting its puzzle-solving algorithm, he turned it loose on a 4000-piece puzzle with only white pieces. Oh, and he had to move his entire shop in the middle of the project.

This set of drawing tools makes it easy to create precise shapes. By combining its parts, you can draw circles, hexagons, triangles, squares, and more. Use it to measure angles with its protractor or long lines with its rolling ruler. Its extendable ruler can be used to draw objects from 0.4″ (10mm) to 18.7″ (475mm) in diameter.

Who says playing cards need to be rectangular? Home Run Games sure doesn’t. Their unique 3-sided cards feature unusual arrangements of symbols and court images, adapted to fit into the triangular constraints. They’re printed on casino-grade linen paper and come in red, blue, or a special limited-edition.

Building on his own his series of dented can sculptures, artist Noah Deledda applied the idea to something you can enjoy every day. The Crushmetric pen changes from a smooth form, to a deeply-faceted pattern with the push of a button. It’s available in a silver or holographic finish. The Action Lab explains how it works.

Barcelona design studio Six N. Five takes us on a journey through time and space represented as a circle moving through various locations. Director Ezequiel Pini says “We are a circle, without boundaries, beginning or end. Infinity, Unity, connection, just a circle in expansion.” Part of the Moco Museum collection.

At first glance, this object looks like a square, but with a quick rotation it transforms into a circle. Physicsfun shows off this intriguing optical illusion created by Matt Enlow. When viewed from the side, you can see it’s actually madeup of four identical parabola segments. A 3D print of the model is available from Shapeways.

Not to be confused with the Phi Ruler, this drawing tool offers another method for drawing with the Golden Ratio, a mathematical ratio known for its ability to produce images and objects with harmony, balance, and structure. The Phi Ruler 2.0 comes in three sizes and in clear or a Bauhaus-inspired color scheme.

Inspired by the geometric star art of John and Jane Kostick, mathematical artist Henry Segerman shows off a neat bit of mechanical engineering which uses a set of five geared racks that can smoothly slide through each other. The model is available as a 3D print from Shapeways, but it’s not cheap.

SAGA is developing an innovative shelter design that could be used by astronauts on the moon. Designed to survive extreme weather conditions, it packs up small for transit and expands to more than five times its original size when opened up. It’s designed to land on-site fully outfitted with furniture, food, water, and resources.

Mathematician and creator Yosuke Ikeda invented this glorious little plaything which uses a series of ramps to move marbles around as you push on it. Multiple AlgoLoops can be combined for more complex patterns. The project’s Kickstarter already has closed, but hopefully we’ll be able to buy these soon.

Artist David Hughes created this incredible light-up showpiece using bespoke 2-way glass mirrors to produce an endless array of patterns. Its custom circuit boards power 960 colorful LEDs, which come to life to produce its hypnotic designs. It’s built with a sturdy, anodized aluminum frame and is limited to 500 pieces.