I shall be rather busy during the next couple of months, so there may be a noticeable drop in the frequency of posts on Complex Projective 4-Space. Nevertheless, I shall endeavour to maintain a steady stream of interesting articles, assuming I have time to do so.

### Puzzle

In the meantime, here is a puzzle Dan Asimov discovered in an obscure journal: *Find a set of n distinct points on the Euclidean plane, such that the perpendicular bisector of any pair of points passes through exactly two points in the set*. I rediscovered the same solution as in the journal, and we believe that this is the unique solution up to similarity. I’ll not post any spoilers yet.

### Rhombic ruminations

I’ll start by explaining the title of this section. The word ‘ruminations’ can refer to deep contemplations, and also to the process by which a ruminant re-digests its food.

In the world of golden rhombi, Christian Perfect constructed a couple of Wieringa roofs at the Newcastle MathsJam following my instructions. His first attempt ended up exhibiting too much positive curvature, but made a decent hat:

### Tessellations of [non]-Euclidean space

Tim Hutton and I are experimenting with different honeycombs for the program Ready. He implemented the triakis truncated tetrahedral tiling recently, and created a couple of Wikipedia pages related to it. You may recognise it as the Voronoi diagram of atoms in a diamond.

We’re also trying out non-Euclidean tessellations. Analogous to the BCC lattice of truncated octahedra in Euclidean 3-space, there is a hyperbolic tiling of truncated icosahedra. There was some discussion about this fifteen years ago. One proof of its existence is its Coxeter-Dynkin diagram, relating it to a known hyperbolic tessellation.