Halloween linkage

John Pai’s art combines woven metal latticework texture with geometric forms (\(\mathbb{M}\)).

Adding the dots from multiple top surfaces allows the design of dice with fewer total dots (\(\mathbb{M}\)).

Pentagonal bipyramids lead to the smallest flexible embedded polyhedron (\(\mathbb{M}\)), new preprint by Matteo Gallet, Georg Grasegger, Jan Legerský, and Josef Schicho. Convex polyhedra are rigid, but some special non-convex polyhedra have at least one continuous degree of freedom. (More than one degree of freedom can be obtained in a trivial way by gluing such polyhedra.) The Bricard octahedra have the same combinatorial structure as a regular octahedron, and can sort of flex, but only if you allow faces that can cross through each other. You can avoid the crossings, for instance by making little gussets near where they would happen, at the expense of making the shape more complicated.

It was believed that Steffen’s polyhedron, with 9 vertices, 21 edges, and 14 triangular faces, was the simplest possible non-self-intersecting flexible polyhedron. For instance, Demaine and O’Rourke’s book Geometric Folding Algorithms (p. 347) writes “As it was later proven that all triangulated polyhedra of eight vertices are rigid, Steffen’s example is minimal in this sense.” But it was apparently not proven, and the new preprint claims a better example: an 8-vertex polyhedron formed from a pentagonal bipyramid by subdividing one triangle into three. This seems a bizarre choice because this subdivision does not affect flexibility. But it can act as a gusset pulling two parts of the boundary away from each other, changing a self-crossing bipyramid into a non-self-crossing subdivided bipyramid.

The fight to make public the scanned data of public-domain 3d artworks in French museums (\(\mathbb{M}\), via), including Rodin’s sculptures.

University library programs that pay a flat licensing fee for commercially published textbooks, in order to keep costs down for students, are disincentivizing and hijacking the funds from programs to produce open-access course materials (\(\mathbb{M}\), archived). These fees do not typically offer students any savings when some of their materials are open-access, and do not typically allow students continued access to the materials once their courses are over.

My RSS reader crashed hard recently; I was behind by two major versions and had to upgrade (\(\mathbb{M}\)). The new version found a few subscriptions from 2017 from an even older version, and I thought I had lost all more recent subs for good, but eventually I found a recent copy of the subscription list buried in a container down eight levels of file hierarchy below my home directory, thanks to a ten-year-old blog post.

So anyway, let that be an excuse for some RSS evangelism. RSS is not dead! Find an RSS reader and use it collect all the blogs and magazines and newspapers and other online sources that you want to keep up with. You can’t read everything, but if you’re going to be enclosed in a bubble, let it be one where you are your own gatekeeper. A couple of explainers, with recommendations for RSS readers: The Verge, Wired (archived).

SODA 2025 accepted papers (\(\mathbb{M}\)).

Predators on predatory journals (\(\mathbb{M}\)). Cabells is as far as I know a legitimate commercial journal analytics company that sells access to a database of predatory journals, which they call “Predatory Reports”. This posting by Cabells reports on an unrelated site calling themselves (at that time) “predatoryreports.org”, maintaining their own separate list and seeking large fees from journal publishers in exchange for removal from the list. I found out about this through a Wikipedia discussion where another editor stated that the publication of this post by Cabells, some nine months ago, had led to a shakeup, of sorts: the predator-of-predators changed the word “reports” in their name to “journals”. Sure enough, now predatoryreports.org redirects to Cabells as it should, but the splash screen for predatoryjournals.org looks pretty much the same as the screenshot from the Cabells post.

Shapes of polyhedra and triangulations of the sphere (\(\mathbb{M}\)), a 1998 paper by William Thurston, provides the following general procedure for making convex polyhedra (or equivalently by Alexandrov’s uniqueness theorem topological spheres with cone singularities) that can be tiled with equilateral triangles, meeting 5 or 6 at a vertex. Draw a (possibly non-convex) 11-gon in a triangular lattice such that equilateral triangles pointing inward from its vertices do not intersect except at the 11-gon vertices. Then the part of the 11-gon between the triangles is a net for a tiled polyhedron (its star unfolding), and every tiled polyhedron can be generated in this way.

AI tool used widely to transcribe medical conversations “is prone to making up chunks of text or even entire sentences” including “racial commentary, violent rhetoric and even imagined medical treatments” (\(\mathbb{M}\)). Because of course it does. The study this news story is based on appears to be “Careless Whisper: Speech-to-Text Hallucination Harms” by Allison Koenecke, Anna Seo Gyeong Choi, Katelyn X. Mei, Hilke Schellmann, and Mona Sloane.

Bob Hearn’s magnetic snap-together 3d-printed stellations of the icosahedra and Scott Vorthmann’s app inspired by these models (\(\mathbb{M}\)).

Dan Piponi rants about Mario Livy feeding quasi-religious misunderstandings of the Fibonacci numbers and the golden ratio by jumping back and forth between examples of other topics such as logarithmic spirals and text about the golden ratio, causing people to think the examples involve the golden ratio when they don’t. Piponi concludes that “it’s deliberate deception in order to sell books”.

• Quickhull on worst-case inputs with unbounded coordinates takes \(O(n^2)\) time, and no better bound is possible.
• Quickhull on random points in a convex region takes \(O(n)\) expected time.
• Quickhull on points with integer coordinates of polynomial size takes \(O(n\log n)\) time.
• Quickhull on inputs whose hull has \(h\) edges takes \(O(nh)\) time.

There was a conjecture from 1996 that the last two of these bounds could be combined: that quickhull on points with integer coordinates of polynomial size and \(h\) hull edges takes \(O(n\log h)\) time. The conjecture is wrong. Quickhull is a divide-and-conquer algorithm that recursively partitions its input in a certain way. The optimality of \(O(n^2)\) can be shown using \(n\) points with exponential coordinates, causing these splits to be highly uneven. The new counterexample is the same construction with \(h\) points, for \(h\) small enough to produce polynomially-large coordinates, plus \(n-h\) points that get carried along for the ride through \(h\) levels of recursion. This shows that the combination of known time bounds \(O\bigl(\min(nh,n\log n)\bigr)\) is optimal for this case.