In this paper, we consider idealized additive multiprimary displays and provide: (a) a complete mathematical characterization for the calibration set, i.e., the set of control values that produce a given color, (b) a subspace decomposition of the device control space that decomposes the control signals into constrained and unconstrained dimensions, and (c) a method for visualizing and analyzing alternative calibration strategies via the representation and the subspace decomposition. Specifically, we demonstrate that the calibration set for a given color is a convex polytope in the device control space whose vertices correspond to alternative tessellations of the gamut in a previously proposed representation. For a K primary display, we decompose the K dimensional control space into a 3 dimensional control visual subspace (CVS) that is completely determined by the desired color and a (K–3) dimensional control black space (CBS) that contains the alternative calibrations within its linear varieties, i.e., affine translations. We use these results for ready visualization and analysis of these sets and of alternative calibration strategies for multiprimary displays. For display technologies such as OLED, where power is switched at the individual pixel level, our methodology reduces the minimum and maximum power calibration strategies to linear programs on polytopes, which are wellstudied and allow corresponding calibrations to be immediately determined as appropriate vertices of the polytopes for calibration sets. The visualizations confirm the intuition that these calibration strategies are not necessarily well-behaved in the presence of device variability we highlight how alternative strategies can be formulated within the proposed framework.