One way to understand complicated 3-dimensional spaces is to cut them into simple pieces.  Conversely, you can build very complicated objects by describing how to glue simple, well understood ones.  My collaborator and I started drawing these egg-like pictures as schematics for this kind of construction, and I thought it would be fun to take the conceit a bit further with an actual egg.  Each egg picture describes what's called a handle structure for a 3-dimensional space, and you can think of this as a set of instructions for building the space, starting from a single ball. There are many ways to build a give space, and you can associate some geometric data to each set of building instructions.  Our work shows that the geometric data you get is independent of which choice of building instructions you select.  This is really useful, because it proves that the geometric data is ultimately about the space itself, not about the process by which it was discovered.

You can find the technical work in our paper, "The Giroux Correspondence in dimension 3" (https://arxiv.org/pdf/2408.01079, joint with V Vértesi).  The egg was made using the Ukrainian pysanky technique, and the tea towel is screen printed on linen.