Geometry Links - July 19, 2026

Probability density map of the single electron of hydrogen
https://x.com/cosmosarcive/status/2075167136067293476

Volume 28, Issue 3 of the Nexus Network Journal, articles selected from the papers presented at the Nexus Conference 2025 in Vicenza, Italy, amidst the extraordinary legacy of Andrea Palladio
https://link.springer.com/journal/4/volumes-and-issues/28-3

All elementary functions from a single binary operator
Paper: https://arxiv.org/abs/2603.21852
Illustration: https://x.com/pickover/status/2075588890006573227

A Neural Sheet Discovers the Shape of Data
https://x.com/mathelirium/status/2075617210135945601

The different forms DNA takes

https://x.com/mathemetica/status/2076310833953755380
Editorial Comment: DNA and the origin of life have been among my tangential interests since high school.
And in recent news: "Scientists have discovered all five canonical nucleobases (adenine, guanine, cytosine, thymine, and uracil)—the fundamental building blocks of DNA and RNA—in pristine samples from the carbonaceous asteroids Ryugu and Bennu. Researchers also found precursor compounds like amino acids and ribose sugars, strongly reinforcing the theory that meteorites delivered the molecular ingredients for life to early Earth.”

The Escherian Stairwell at Rochester Institute of Technology
https://www.youtube.com/watch?v=iBY4HaAngaA

Patterns set by Bessel function zeros
https://x.com/mathemetica/status/2076705550688211241

Spinning the Yin/Yang symbol
https://x.com/Rainmaker1973/status/2077050486906065198

Orbital resonance in the solar system
https://x.com/cosmosarcive/status/2077326272775217498

Resonance nodes on a circular plate - cymatics in 2 & 3D
https://x.com/mathemetica/status/2078170771269341501

Weird geometry, kisrhombille, forsythia, whelmer, drifter, writher, clouder, powerbox, source, documentation, animations and graphics
https://fleen.org/
hat tip Cliff PIckover

Physical realities beyond the Standard Model
https://x.com/Dragonmaurizio/status/207849040229510770

Editorial Comment: I’m seeing more interesting geometry in my feeds these days. Ideas are exploding it seems.

Geometry Links - July 10, 2026

Sand watch
https://x.com/spydenator/status/2062867816534143162

Icositetrahedron with twelve regular heptagonal cross-sections
https://www.facebook.com/reel/1721999075896555
hat tip Kirby Urner

Skeleton of a stingray
https://www.tumblr.com/wewantnothing2/819977959294337024/the-skeleton-of-a-stingray

Mesh Module
https://designawards.core77.com/Toys-Play/143113/MeshModule-A-Playful-Modular-Mesh-System-for-Creative-Construction

Complete notebooks of Leonardo da Vinci now online
https://teche.museogalileo.it/leonardo/ricostruzioni/index.html?lang=en

Gerald De Jong’s "mobile tensegrity at scale"
https://www.facebook.com/photo?fbid=10164141494898948&set=pcb.10164141517248948
https://fluxe.art/

Monorhaphis Chuni - the structure of an 11,000 year old deep sea sponge
https://timesofindia.indiatimes.com/etimes/trending/this-deep-sea-creature-can-live-up-to-15000-years/articleshow/115060151.cms

Polyèdres et particularités mathématiques
https://www.facebook.com/groups/196165767185827/

A common roadmap for mathematical models of brain rhythms
https://x.com/VFD_org/status/2073180094835589537
https://x.com/VFD_org/status/2073180094835589537/photo/1

Canonical Projection Tiling (4 → 2)
https://edmund.mathematicians.org.uk/shaders/4to2CPT/

Visualization of the building blocks of matter in a dynamic 3D spiral
https://x.com/mathemetica/status/2075199649443643770

Zernike polynomials Z_n^m form an orthogonal basis set over the unit disk
https://x.com/mathemetica/status/2074936053304320113

Geometry Links - June 6, 2026

Growth ratio set in motion
https://x.com/mathemetica/status/2049938085345972598
Thread on Riemann Hypothesis
https://x.com/mathemetica/status/2050084790918107396
Editorial Comment: @mathemetica does good work

Local universe fly-through of 55,486 galaxies
https://x.com/S_Conradi/status/2050292756619166006

Stable three-body solutions
https://x.com/Rainmaker1973/status/2050242433099731261

A short history of geometric Algebra by Tim Havel
https://web.mit.edu/tfhavel/www/IAP-02/lect1.pdf

A Tensegrity-Based Side Table Made out of Pipes
https://www.core77.com/posts/143987/A-Tensegrity-Based-Side-Table-Made-out-of-Pipes
More Pipe DIY at https://www.instagram.com/pipepipediy/

Mapping birdsong
https://x.com/pascal_bornet/status/2051165179883528280

Square to triangle
https://x.com/olurkanka/status/2052821752468627656

The geometry of butterfly eggs
https://bsky.app/profile/ariaa.bsky.social/post/3mlntqbhbx22j

Charting Aquinas' Summa Theological and the Catholic Liturgical Calendar
https://owen-cyclops.myshopify.com/

Anthony James geometric reflections
https://bsky.app/profile/arepublic86.bsky.social/post/3mlu2c6arqk2a
https://www.anthonyjamesstudio.com/

Neither zero nor one but a third state, qutrits in quantum theory
https://www.facebook.com/photo?fbid=122217749198545093&set=a.122112138236545093
https://www.youtube.com/watch?v=ipSxO6UIs3I
hat tip: Bob Whelan

Suspension-Based Outdoor Chair - not quite tensegrity but...
https://www.core77.com/posts/144235/Sagas-Transat-a-Suspension-Based-Outdoor-Chair
https://saga.now/

Geometry Links - April 2026

Gaosu Sheying’s slow motion art
https://x.com/IntVideos_x/status/2036445478468956476

The Plenum-to-Particle Loop Sequence of Field Structure Theory (FST) by Don Bridell
https://fsi-group.mn.co/posts/97325920

The Splash of a Drop
https://publicdomainreview.org/collection/the-splash-of-a-drop-1895/
hat tip Cory Doctorow

Harmonious Geometry: The Hirajoshi Wave
https://x.com/mathemetica/status/2045190962364956840
hat tip Lucas Gonzalez

A streamlined paper plane
https://x.com/buzz_video_buzz/status/2045363954025926909

Extruded cubic cells (24 faces, 36 edges) tessellated via snapology origami
https://x.com/mathemetica/status/2046092594162373007
Editorial Comment: from Harvard but I wonder if anyone there still remembers Dr Arthur Loeb and his Design Science course, let alone the Philomorphs

The stars from Mars
https://x.com/MindProbe/status/2046394310396940665/photo/1

Cellular landscapes
https://www.reddit.com/r/CrazyFuckingVideos/comments/1sxgtw8/the_crowded_interior_of_a_cell/
https://gaelmcgill.artstation.com/projects/Pm0JL1
https://www.digizyme.com/cst_landscapes.html
hat tip Massimo@Rainmaker1973

Jon Foreman's Rock-Based Land Art
https://www.core77.com/posts/143878/Jon-Foremans-Rock-Based-Land-Art

Penrose Triangle
https://x.com/Y4lP2012/status/2049512113727504834

Luca Pacioli’s Rhombicuboctahedron: Description, Construction, and Architectural Reception
https://link.springer.com/article/10.1007/s00004-026-00885-9

Ice XXII - the most recently discovered form of ice with a crystal structure which repeats its pattern every 304 molecules
https://www.quantamagazine.org/physicists-discover-the-most-complex-forms-of-ice-yet-20260427/
hat tip boingboing.net

Geometry Links - March 25, 2026

Puzzlebomb 2 & 3 D jigsaw puzzles
https://puzzlebomb.com/collections/browse-all-puzzles

Star 3D Sensory Fidget Toy
https://www.tiktok.com/@george_grm/video/7532161413297638658

Ruth Asawa exhibition at MOMA, photographs by Elizabeth Resnick
https://www.facebook.com/photo?fbid=10225437769486204&set=pcb.10225437776886389

Ulam’s spiral of primes
https://x.com/PhysInHistory/status/2015029114621804612

Resolving a topology puzzle
https://www.quantamagazine.org/two-twisty-shapes-resolve-a-centuries-old-topology-puzzle-20260120/
hat tip to boingboing.net

Rinus Roelofs’ Compound of 5 Tetrahedra to Tetrahelix
https://www.facebook.com/reel/935963982231517
and Icosahedron to Tetrahelix
https://www.facebook.com/reel/2570762116675763

Hypertiles toy
https://funinmotiontoys.com/products/hypertiles

Kirby Urner’s Cascadian Synergetics
https://docs.google.com/presentation/d/1zcJsWYuV_DW1HKZirsoufacPMNlXQgWoYHeYPOPS1kY
https://www.youtube.com/watch?v=4G0sHXgpZxA

Visualizing Climate Conference 2026 - Bologna, Italy, November 4-6
https://climate.copernicus.eu/visualising-climate-2026

Mapping all the connections in a fly’s brain
https://www.nature.com/articles/s41586-024-07686-5
BBC article: https://www.bbc.com/news/articles/c0lw0nxw71po
If you meet a paywall: https://archive.ph/ivKQL

Beading with Algorithms: Cellular Automata in Peyote Stitch - "Can you weave beads so that each new stitch you take depends upon what you have already beaded? To answer this question, we explore how the mathematical concept of one-dimensional cellular automata can be applied to beaded peyote stitch, in other words, beading with algorithms.”
Beading With Algorithms: Cellular Automata In Peyote Stitch by Gwen Fisher, Roger Antonsen, Zelda Lin (Artist)
https://www.worldscientific.com/worldscibooks/10.1142/14357#t=aboutBook
30% off code: RECMATH30

Icosahedral wind machine
https://www.instagram.com/reel/DV0zPcUj-FG/?igsh=cjBqY3NhNWJiYTlt
https://www.instagram.com/geowind.kr/
https://geowind.kr/
hat tip to Marshall Spriggs
Editorial Comment; I wonder if it can go through a Jitterbug transformation

Geometry Links - January 10, 2026

Angela Cupertino - scholarship winner at Pacific Coast OrigamiUSA Conference 2025
https://www.facebook.com/photo/?fbid=1128729186042290&set=a.502627711985777

Kinetic furniture
https://www.core77.com/posts/139276/Experimental-Kinetic-Furniture-Design-Aaron-Preyers-Blooming-Project

AI that builds machines called Noyron trained a Large Computational Engineering Model [LCEM] and designed his hypersonic precooler which uses a fractal folding algorithm to chill down superheated air
https://x.com/BrianRoemmele/status/1989759968959156297
hat tip Karl Thideman

8th grader Miles Wu folds origami that can hold over 9000 times its own weight
https://www.youtube.com/watch?v=QCODaKLzL-w
hat tip to boingboing.net

283 trillion colors of fractals
https://www.facebook.com/reel/1988387765038458
hat tip Vinay Gupta

The mountains of Pluto
https://x.com/MAstronomers/status/2005055593502179767

Best Northern Lights photography of the year - the geometry of our electromagnetic atmosphere
https://capturetheatlas.com/northern-lights-photographer-of-the-year/

Natural motion of a pendulum
https://x.com/Saganismm/status/2007795854145712410

New Kosticks design
https://www.facebook.com/watch?v=1540874743631158

Aqua Swimming Sea Bike
https://x.com/SalmanGreen/status/2009188815756480841

Frost flowers
https://www.instagram.com/p/DRuTEkoEWTP/
hat tip to boingboing.net

Robert Fathauer mathematics art
https://www.mathartfun.com/robertfathauer.com/index.html

Geometry Links - Halloween 2025

Geometric and mandala programs
https://www.omnigeometry.com/

Tesla valve - a fixed-geometry passive check valve
https://x.com/Rainmaker1973/status/1965645158734557427

Two from Daniel Ari Friedman
Quadmath
Code: https://github.com/docxology/QuadMath
Paper: https://zenodo.org/records/16887800 QuadMath: An Analytical Review of 4D and Quadray Coordinates
QuadCraft -- this is a (functional) work in progress, it is a browser-based video game that is like "MineCraft but in the Isotropic Vector Matrix (close-packed spheres) rather than Cubic setting"
https://github.com/docxology/QuadCraft/

Callen Schaub artworks
https://www.facebook.com/reel/1147623173958331
https://callenschaub.com/
hat tip Nathan Koenig

Truncated Icosidodecahedron in Beads Crater Moon Beaded Bead
https://gwenbeads.blogspot.com/2017/12/truncated-icosidodecahedron-in-beads.html?m=1
Whole Movement - folding circle geometries
https://www.wholemovement.com/
https://www.wholemovement.com/gallery

A box with a reversible butterfly lid
https://www.core77.com/posts/138856/A-Box-with-a-Reversible-Butterfly-Lid\

Kirigami parachutes
https://www.core77.com/posts/138862/Inexpensive-Inside-Out-Parachutes-Based-on-Kirigami

Jeremy Frey - 2025 MacArthur Fellow - basketry weaver artist
https://www.youtube.com/watch?v=e_PBNBFM-_g
https://jeremyfreybaskets.com/

NYTimes on the Bridges Conference, featuring the work of Rinus Roelof
https://www.nytimes.com/2025/10/10/science/mathematics-art-roelofs.html
If you meet a paywall try: https://archive.ph/Uhige

Ghee Beom Kim digital geometric art
https://www.facebook.com/ghee.b.kim/reels/

Ekaterina Lukasheva kusudama.me with Klara Mundilova @klara.mundilova made for an exhibition “Connecting Artifacts” at @tachi.tomohiro lab.
https://www.facebook.com/watch?v=1154415900127186