. . . muttered the ogre

After installing that matrix math library, I spent a week’s evenings pushing several abstract graphs through my “topological coordinates” program and finding, to my lack of complete shock, that none of them had any neat three-dimensional embedding.

Then I tried a torus, and was again far from amazed that it didn’t work well either: all the vertices being equivalent under the inherent symmetries, there’s nothing to distinguish the “inner” from the “outer”.

I cut a seam of the torus to make a cylinder, and then I got a surprise: the free ends curl in like an apple. If anything I’d expect the opposite: the vertices along the edges, being topologically outermost, “ought” to curl outward.

One of these days I’ll get around to fullerenes.