Petersen-Embellished Non-orientable Blanket Square
(exhibited at the 2017 JMM)
This piece arose from an interdisciplinary challenge to represent one’s research as a blanket square. As a topological graph theorist, I study graphs embedded on surfaces. One can remove a disk from any surface and stretch/manipulate the resulting boundary into an “exterior” square, so in theory any embedded graph could become a blanket square. However, to be of use in a blanket the finished square must not be unwieldily thick or rife with gaping holes; thus, the surface must have low genus. I chose to work with the projective plane, and to embed the Petersen graph. Because this surface is nonorientable, there is no “front,” and so the finished square can be viewed equally from either side.