A few of the many triply periodic minimal surfaces can be generated from a quadrilateral slice through a tetrahedron of mirrors, as refined by Surface Evolver. I had the idea that the same concept, applied to one of the analogous tetrahedra that tile spherical 3-space, could result in a pretty model.

To my disappointment, none of the non-prismatic kaleidoscopes — those that generate the six regular polychora — hosts a nondegenerate minimal surface (of this simple form); but each of the duoprism kaleidoscopes gives at least one.

(2018) One could try minimal surfaces with the constraint of partitioning into equal volumes, if one understood how to specify such a constraint in non-Euclidean space. Apparently it needs a metric tensor, whatever that is.

This one is a projection of a design on (half of) the surface of a hypersphere: a ribbon spans two orthogonal great circles, wrapping three times around one and five times around the other.

Kitty teeth did break it at one point, but with redundancy that’s not a serious problem. Having got my pix I’ll keep the new toys away from them henceforth.

Not only did it not fall apart in my hands …

The strand — for it is a Klein bottle woven of a single strand — is thinner than I expected, and has broken in at least two places. Ah well, live and learn; I’ve already redesigned it to be more robust.

I came up with this concept several years ago (I can’t tell exactly when, because I’ve mislaid the original code!) but never posted any of the images until now.

Some of you may like to guess what’s going on before I tell. For more hints, see these patterns’ 254 siblings.

I made some progress on an old project: to make outline fonts based on some favorite old bitmap fonts, by automatic fitting of smooth curves to the sequences of dots.

(The image above is in Scalable Vector Graphic format. If you see nothing, you may – dare I say it – need to update your browser. It works in Firefox 5, Safari 5, Chrome 12, Kindle.) ( . . more . . )

My newest incoming link is from Wendy Krieger, whose site you should definitely see if you’re interested in polytopes, duodecimalism or the letter Þ.