Displays that render colors using combinations of more than three lights are referred to as multiprimary displays. For multiprimary displays, the gamut, i.e., the range of colors that can be rendered using additive combinations of an arbitrary number of light sources (primaries) with modulated intensities, is known to be a zonotope, which is a specific type of convex polytope. Under the specific three-dimensional setting relevant for color representation and the constraint of physically meaningful nonnegative primaries, we develop a complete, cohesive, and directly usable mathematical characterization of the geometry of the multiprimary gamut zonotope that immediately identifies the surface facets, edges, and vertices and provides a parallelepiped tiling of the gamut. We relate the parallelepiped tilings of the gamut, that arise naturally in our characterization, to the flexibility in color control afforded by displays with more than four primaries, a relation that is further analyzed and completed in a Part II companion paper. We demonstrate several applications of the geometric representations we develop and highlight how the paper advances theory required for multiprimary display modeling, design, and color management and provides an integrated view of past work on on these topics. Additionally, we highlight how our work on gamut representations connects with and furthers the study of three-dimensional zonotopes in geometry.
