The evolution of a particular sensory organ is often discussed with no consideration of the roles played by other senses. Here, we treat mammalian vision, olfaction and hearing as an interconnected whole, a three-dimensional sensory space, evolving in response to ecological challenges. Until now, there has been no quantitative method for estimating how much a particular animal invests in its different senses. We propose an anatomical measure based on sensory organ sizes. Dimensions of functional importance are defined and measured, and normalized in relation to animal mass. For 119 taxonomically and ecologically diverse species, we can define the position of the species in a three-dimensional sensory space. Thus, we can ask questions related to possible trade-off vs. co-operation among senses. More generally, our method allows morphologists to identify sensory organ combinations that are characteristic of particular ecological niches. After normalization for animal size, we note that arboreal mammals tend to have larger eyes and smaller noses than terrestrial mammals. On the other hand, we observe a strong correlation between eyes and ears, indicating that co-operation between vision and hearing is a general mammalian feature. For some groups of mammals we note a correlation, and possible co-operation between olfaction and whiskers.