Mutual voronoi tessellation in spoke pattern convection

Planar cellular networks are made of polygonal cells usually having an average of six sides and trivalent vertices. We analyze the topological properties of spoke patterns observed in the convection of highly viscous fluids. The competition between ascending and descending columns of fluid generates dual networks where on average cells are four sided and vertices tetravalent. This observation identifies a new class of dual networks satisfying a mutual Voronoi relation. The metric of the pattern is dominated by the distance between nearest neighbors vertices of opposite species.