Giving a continuation to our work to understand the characteristics of the tristimulus values in colors obtained by subtractive color mixture, we extend several theorems provided in our previous articles. Previously, we started proving theorems for a single dimension, considering only individual tristimulus values. In the present article, the one-dimensional discussion is extended to the three-dimensional discussions of the tristimulus space. These theorems establish the absolute lower and upper hounds for tristimulus values of subtractive color mixtures of the ideal color. The results contribute toward a comprehensive modeling of subtractive color mixture. (c) 2005 Wiley Periodicals, Inc.