A spanner is a mathematical structure that can sometimes be found inside another. (More specifically, a spanner is a spanning subgraph with certain "good" distance properties.) This image shows the structure of part of a spanner of a three-dimensional torus graph.

I have about eight or nine papers on spanners, all with my coauthor and fellow polymath Art Liestman. The ones we've been working on lately, such as the one shown here, are in graphs with three-or-higher-dimensional structure, which means, amongst other things, that even a three-dimensional visualization of them can get quite confusing. I had to keep the spanner in this image extremely small, so that there wouldn't be too much visual clutter.