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Henry Segerman

@henryseg

Mathematician and mathematical artist/maker. segerman.org, http://youtube.com/@henryseg, https://mathstodon.xyz/@henryseg

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14.01.2025
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Latest posts by Henry Segerman @henryseg

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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.

01.03.2026 23:29 👍 2 🔁 0 💬 0 📌 0

High order sphericon?

01.03.2026 16:17 👍 2 🔁 0 💬 1 📌 0
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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

13.02.2026 16:31 👍 36 🔁 6 💬 0 📌 1
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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)

11.02.2026 15:42 👍 6 🔁 5 💬 1 📌 0

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

01.02.2026 17:50 👍 0 🔁 0 💬 0 📌 0
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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.

24.01.2026 21:47 👍 1 🔁 0 💬 0 📌 0
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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!

24.01.2026 21:47 👍 10 🔁 1 💬 1 📌 0
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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/...

20.01.2026 09:01 👍 2 🔁 0 💬 1 📌 0
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.

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 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.

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 ☺️

11.01.2026 22:45 👍 67 🔁 16 💬 5 📌 0
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.

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

08.01.2026 15:56 👍 8 🔁 3 💬 0 📌 0
Bridges 2026 Call for Submissions – The Bridges Organization

🚨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

04.01.2026 15:49 👍 11 🔁 7 💬 1 📌 2
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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

30.12.2025 16:42 👍 18 🔁 5 💬 0 📌 0

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

20.11.2025 00:11 👍 0 🔁 0 💬 0 📌 0
A doorway into the safe, with a pattern of light and shadow visible inside.

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.

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.

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.

20.11.2025 00:11 👍 15 🔁 1 💬 2 📌 0
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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.

09.11.2025 16:34 👍 61 🔁 12 💬 4 📌 1
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Understanding geometry through model making

06.11.2025 17:51 👍 46 🔁 14 💬 2 📌 2
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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...

05.11.2025 05:07 👍 7 🔁 4 💬 0 📌 1
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Every Artist Has a Favorite Subject. For Some, That’s Math.

There's a nice article by Siobhan Roberts about the Bridges 2025 conference in Eindhoven in the NY Times. I can now say that I am in The NY Times! (A photo credit for the shot of Chaim Goodman-Strauss and Edmund Harriss,... but still!) www.nytimes.com/2025/10/10/s...

10.10.2025 19:20 👍 28 🔁 10 💬 1 📌 0
A dark-themed event poster titled "EXPLORING ZETA FUNCTION VISUALIZATIONS." The poster includes an abstract about visualizing the Riemann Zeta function. A colorful, three-dimensional plot of a mathematical function dominates the right side. The bottom features a circular photo of the presenter, Grant Sanderson from 3Blue1Brown. The event is scheduled for Friday, October 10, with times listed, and will be held on Zoom.

A dark-themed event poster titled "EXPLORING ZETA FUNCTION VISUALIZATIONS." The poster includes an abstract about visualizing the Riemann Zeta function. A colorful, three-dimensional plot of a mathematical function dominates the right side. The bottom features a circular photo of the presenter, Grant Sanderson from 3Blue1Brown. The event is scheduled for Friday, October 10, with times listed, and will be held on Zoom.

The #illustratingMath Seminar Online returns on Friday, October 10th, 9 am Pacific / 12 pm Eastern / 6 pm Europe. @3blue1brown.com will be "Exploring Zeta Function Visualizations." Gabriel and Jim will provide some "Show and Ask" input. See you online on Friday!

06.10.2025 15:35 👍 7 🔁 4 💬 0 📌 0

@robertfathauer.bsky.social ?

26.09.2025 02:57 👍 0 🔁 0 💬 0 📌 0
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Submissions are now being accepted for the Exhibition of Mathematical Art to be held as part of the Joint Mathematics Meetings, Washington, DC, in January of 2026. Apply online through October 15 at gallery.bridgesmathart.org. pic.x.com/MGSEyexSzo

25.09.2025 20:35 👍 17 🔁 9 💬 0 📌 1
The Bridges Archive: 2024 paper

This sounds like a similar idea to a project by Jeffrey Ventrella, see archive.bridgesmathart.org/2024/bridges... I don’t think he looked at fairness, and he made polyhedra with the points as vertices rather than faces.

25.09.2025 20:16 👍 2 🔁 0 💬 1 📌 0

Correct. And rigging up the slider at that angle would not be easy either!

25.09.2025 17:21 👍 2 🔁 0 💬 0 📌 0
Photograph of a camera with a probe lens mounted on a slider.

Photograph of a camera with a probe lens mounted on a slider.

Just added a post with some of the behind the scenes details and unused footage from this video on my Patreon: www.patreon.com/HenrySegerman

25.09.2025 15:13 👍 3 🔁 0 💬 1 📌 0
The Dice Lab Unique Designs

You can buy these at www.mathartfun.com/DiceLabDice....!

24.09.2025 18:35 👍 5 🔁 0 💬 1 📌 0
Dice with greek letters on the faces, on a sheet of paper with a very long equation on it.

Dice with greek letters on the faces, on a sheet of paper with a very long equation on it.

New dice from The Dice Lab (me and Robert Fathauer), which may (?) be useful if you regularly write equations. youtube.com/shorts/fgMox...

24.09.2025 17:11 👍 50 🔁 13 💬 3 📌 5

It’s a single loop.

15.09.2025 12:31 👍 2 🔁 0 💬 1 📌 0

In this image, our algorithm fills the sphere much more completely than Thurston's does, despite using ten times fewer edges.

14.09.2025 20:19 👍 4 🔁 0 💬 0 📌 0

The black curve is our recreation of Thurston's original algorithm to approximate Cannon-Thurston maps. The boundary between the green and purple regions is an approximation generated by our new algorithm based on veering triangulations.

14.09.2025 20:18 👍 5 🔁 0 💬 2 📌 0
A very squiggly black curve on a sphere. The sphere is divided into green and purple regions by a less squiggly, but more sphere-filling curve.

A very squiggly black curve on a sphere. The sphere is divided into green and purple regions by a less squiggly, but more sphere-filling curve.

This image (made with Saul Schleimer) shows two different ways to approximate the Cannon-Thurston map associated to the figure-eight knot. Cannon-Thurston maps are space-filling curves, a bit like the Hilbert curve except that these fill a sphere rather than a square.

14.09.2025 20:17 👍 35 🔁 6 💬 3 📌 1