Topology of plane sections of periodic polyhedra with an application to the Truncated Octahedron

Abstract

The main results of A. Zorich and I. Dynnikov about plane sections of periodic surfaces are extended to the PL case. As an application, the Stereographic Map of a truncated octahedron, extended to the whole $\Rt$ by periodicity, is analyzed numerically.

40 pages, 30 figures

References in corpus (3)

• First-principles generation of Stereographic Maps for high-field magnetoresistance in normal metals: an application to Au and Ag
• Infinite Periodic Discrete Minimal Surfaces Without Self-Intersections
• Characterization of the set of "ergodic directions" in the Novikov's problem of quasi-electrons orbits in normal metals