A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots | Quanta Magazine With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots.

Mathematicians have built beautiful, snowflake-like codes to untangle some of the trickiest knots. @ericaklarreich.bsky.social reports: www.quantamagazine.org/a-powerful-n...

It’s possible, although I may want to shrink some components when I give that a try!

Here's a second, geared mechanism that transforms between cube and octahedron forms. Full video at youtu.be/T9BNMLFHXUw

This is a result of our fabulous #illustratingMath trimester at the institute Henri Poincaré in Paris, which ran from January till March this year. Attached is an image of the piece in the #art exhibition at the Maison Poincaré. Definitely give Henry's video a look!

Good question!

I haven’t made any of them but they are just sitting there in the platonic realm. I think that a dodecahedron/icosahedron linkage would be even more unruly than the cube/octahedron one. The geared version should work, although it would be a big mechanism!

New video, on mechanisms that illustrate the duality between the cube and the octahedron! Here's one of them: a linkage with fabric panels designed by Sabetta Matsumoto.
Full video at youtu.be/T9BNMLFHXUw

Too easy… the effective frustum is everything, so it doesn’t matter where you are relative to the rest of humanity.

They are in the frustum of the camera’s view. I think that’s the idea.

I wonder how easy it would be to take a photo with everyone else in the frustum without a space mission. Seems like it should be possible with a fisheye lens up high if you wait for any passing planes or space stations.

Cube net folding.

There is research on fabricating micropolyhedra using lithographic techniques via self-assembly / self-folding of nets that fold to, e.g., a cube as illustrated. Note the tiny size: 0.2mm. The goal is to minimize mis-foldings.
doi:10.1371/journal.pone.0004451 cs.smith.edu/~jorourke/Ma...
#MathSky 🧪

A very similar pattern to Robert’s post, on another driveway.

I took this photo in Heidelberg a decade ago. I wonder how many driveways have it globally!

We’ve been experimenting with the transparency toolkit from HeyGears to create optically clear models of radiolarians, microscopic single-celled marine organisms that build intricate glass skeletons with stunning geometric complexity. #sciart #3dprinting
(Printer + materials provided by HeyGears)

Poster: Beach Spectres, we want to make the largest aperiodic tiling ever! What's an aperiodic tiling? It's when you cover a flat surface with copies of a shape like the one above, without any repeating patterns. The Spectre monotile was only discovered in 2023, and mathematicians are really excited about it! What are you doing? We're going to use large “cookie cutter” tools in the shape of the Spectre to cover the beach with the aperiodic tiling. You can help: come to the beach and we'll show you what to do. Where and when? Whitley Bay beach, 7th June 2026. Come and join in, just watch, or talk to some very enthusiastic mathematicians! beachspectres.com

I'm enormously happy to finally be able to announce the date of the #BeachSpectres project: 7th June, 2026. #WhitleyBay beach, UK.

If you can make it to the beach and join in with the tiling effort, I'll be very happy to see you and glad of the help!

Lots […]

[Original post on mathstodon.xyz]

Polysphericons - HITS Polysphericons are solids which can be obtained from polygons with a revolution, cutting in half and gluing back together. One commonly ...

Here’s one write up I found of different sphericon designs: www.h-its.org/projects/pol... It looks like your curves are the cores of the “faces” of the sphericons.

High order sphericon?

HyperRogue is now verified for SteamDeck! ✅

A perfect game/platform match: mostly only movement so no need for complex buttons, joystick is good for its non-Euclidean movement directions, bigger screen and more powerful hardware are a better fit for infinity than phones.

#roguelike #steamdeck

Things have been rather busy at the #illustratingMath trimester at the Institut Henri Poincaré for the last two weeks. A number of illustration projects have been started. I'll share some highlights in this thread. (1/6)

Is it the same acquaintance? Are you sure they’re not stalking you?

Reconfigurable polyhedral mechanisms using scissor-like elements with cantellation transformation between dual geometries Deployable polyhedron mechanisms (DPMs) have garnered significant interest in architecture, aerospace, and robotics, where reconfigurable and space-ef…

The paper (www.sciencedirect.com/science/arti...) by Liao, Kiper, and Krishnan has lots of other interesting mechanisms, including one showing duality between the cuboctahedron and the rhombic dodecahedron.

Earlier this week I was challenged to come up with a mechanism that would illustrate the duality of the cube and the octahedron. I got as far as making this animation before discovering that I was scooped three months ago!

Save 20% on BroomSweeper on Steam BroomSweeper is a Minesweeper-style Roguelike puzzle game. Unmask the evil lurking at TentaTech, Inc. as you ascend through increasingly challenging floors. Assemble winning combinations from over 100...

Minesweeper roguelike I’ve been having a lot of fun with out in full release now: store.steampowered.com/app/3473250/...

My featured-artist display at JMM 2026 in Washington DC. Four of the works are hanging on a zig-zag of beige, custom-cut mats, and the fifth is on three black jewelry stands. All pieces were accepted into one or more juried exhibits at JMM or Bridges in the past decade. The blue knitted wall hanging, second from the left, is the solo piece that was accepted into this year’s exhibition.

A closer view of the first two panels of the folded mat backing. The three pieces were 28 inches tall and 14, 28, and 28 inches wide, which is bigger than it sounds when you’re carrying them. On the left is Fundamental Frieze Scroll II from 2018, a tan knitted wall hanging which was the precursor for the new piece to its right. That new piece, The Fundamentals of Lace, is knitted in blue on smaller needles but is both wider and taller than the older work. Both wall hangings are composed of the same fundamental region, a small lace motif in a lambda or Y shape, and both have colored beads embedded in the fabric to mark the symmetries. For more details, go to the following post for the online catalog links.

A close up of the rightmost mat panel and the jewelry set. As before, for more details you can follow the catalog links in the following posts. The last mat panel has two knitting wall hangings suspended from pins at the top of the panel. To the left is Float Free, Bumblebee, a wall hanging in two-color mosaic knitting with yellow and black yarn. Like the two pieces in the previous photo, the knitted fabric is rectangular and lashed to dowels at the top and bottom. The fabric is divided into horizontal and vertical strips with different repeating abstract designs. On the right of the mat is Redistribution, a wall hanging that has the overall shape of an hourglass whose top segment is shorter than the bottom segment. The upper portion is fan-shaped, with a network of dark purple stitches over a background of pale green stitches. The lower portion is flared like a trumpet and juts away from the wall, with a network of light purple stitches on a background of dark green. To the right of the folding backdrop is Map Coloring Jewelry Set, the oldest artwork in this display. A bead crocheted necklace with pendant, a bead crocheted bracelet, and bead woven earrings in eight matte colors with gold accents hang on a black necklace form and black bracelet and earring stands. This jewelry set won a prize in the JMM 2015 exhibit, and now and then, I still wear it.

#mathart #mathknitting #JMM2026

This year, the math art exhibition at the Joint Mathematics Meetings invited me to be a featured artist, giving me the chance to assemble this mini-retrospective of my knitted and beaded work. Links to the catalog entries are in the following posts.

🧶 #knitsky ☺️

Mathematical objects (polyhedra, fractals, hyperbolic surfaces, etc.) on a grand piano under a black cover. In the background: an overhead projector, ventilation grids, the bottom of a screen and of a blackboard. Behind the picture window, a concrete mixer next to a low wall that is being built.

A grand piano, a concrete mixer, an overhead projector, and an eclectic selection of mathematical objects. 🤩 @cirm-math.bsky.social #illustratingMath

🚨The call for submissions for this year's @BridgesMathart conference is out: www.bridgesmathart.org/b2026/bridge....

Regular papers: 1 February
Short paper: 1 March
Workshop papers: 1 March
Artworks: 15 March
Math + Fashion Show: 15 April
Short Film Festival: 09 May
Family Day: 15 June

New video out just now, on a mechanism that uses racks and gears to expand and contract, this time in all three dimensions! youtu.be/NEJZlGuWGV8

Museum preparator Michael King was testing the mounting system today and invited me along to check it out!

A doorway into the safe, with a pattern of light and shadow visible inside.

A 3D-printed sphere is patterned with triangular holes. It casts shadows onto the wall.

Closeup of the 3D printed sphere. It is mounted on a pipe coming down from the ceiling, which also holds an LED light.

The OSU Museum of Art is in a beautiful old building that used to be a post office. They have a small but heavily-fortified room that used to be a safe. Not such a great location to view paintings, but will work nicely for light-based sculpture, like "(5,3,2) triangle tiling", by @saulsch and me.

Giant cardioid: version 2.5. Version 1.0 was made using Pex tubing and grommet tape. Version 2.0 was made from laser-cut pieces. The wood was too fragile, and it broke during construction. In version 2.5, I made the pieces wider and I used thicker wood. Success, I'd say! The diameter is about 5 ft.

Understanding geometry through model making

Everyone is invited to attend the SCULPT 2025: Show & Tell, a digital gathering that celebrates creative exploration across art, geometry, design, and fabrication.
Date: Friday, November 7, 2025
Time: 8:00 – 10:30 AM (PST)
Zoom Link: cca.zoom.us/j/9826107944...