Representing More than Three Contingencies

According to M-Phi: "Only three (and no more) co-ordinate axes can be placed perpendicularly to each other".  However, I find, that if the axes are bent and conceived to be spherically perpendicular (e.g. still dividing quadrants), then there may indeed be higher-dimensional exceptions to the three-dimensional rule. This is conventionally the domain of the hyper-cube, but factually, representations in this sense seem conceptually possible which are not merely three-dimensional, nor are dynamic in the fourth. Here is a diagram demonstrating: