Discrete conformal structures and generalized hyperbolic polyhedra

Discrete conformal structures can be defined axiomatically as generalizations of deformations of (generalized) circles with fixed (generalized) intersection angles. Circles can be represented as (projective) space-like points in Minkowski 4-space, so these can be generalized to light-like and time-like points. Intersection angles can be generalized via the Minkowski product to include inversive distances between (space-like) circles or distances between (time-like) points in hyperbolic space. We will discuss this viewpoint, where we as 2D Euclidean (or hyperbolic or spherical) beings live on the section (generalized angle) of a hyperbolic polyhedron. This is preliminary work with Illia Hayes.