Aperiodical News Roundup – August/September 2026

Here’s a round-up of some news from the last couple of months. Mathematical discoveries Lerch primes are defined as odd primes that divide their Lerch quotients (obviously) and until now we only knew four of them existed. This month, Veljko Vranić has found the fifth Lerch prime: it’s 42,447,347, if you were wondering. (via the SeqFan mailing list) Ruslan Mizhaev has written about an octahedron of genus 3 which is equivelar (all vertices have the same degree and all faces the same number of edges). The author had first described the shape in 2020 – the new work gives coordinates for vertices and equations for edges so we can check it’s really a polyhedron. A new 3D aperiodic monotile has been discovered, based on the existing ‘chair’ substitution tiling which consists of a cube with a cube-shaped corner missing, 8 copies of which can be arranged to make a larger copy of the original shape (and extended to a tiling of 3D space, which can be periodic). (Image below from the Chair tiles…