Sensory coding in olfaction remains poorly understood. Unlike in vision, where the stimulus space is well-characterized, the complexity of the "odor space" and the complexity of the olfactory receptor (OR) repertoire has hindered our understanding of odor coding and processing. There is no consensus on key defining features of odor sensation, such as the dimensionality of odor perceptual or odor receptor space. It is commonly conjectured that the ORs transform the high-dimensional "chemical space" to a relatively low-dimensional space of neuronal representations. We developed a novel method for the inference of a stimulus space from neural activity. This method makes no assumptions on the underlying stimulus space; instead it assumes that the receptive fields are half-spaces in some natural coordinate system in the underlying olfactory space. A key feature of this method is that it is insensitive to the inherent (and unknown) monotone non-linearities of neuronal responses. It turns out that it is possible to infer the stimulus space from the noisy and sparse data that is available for the activity of olfactory receptors in flies and mice. Our method converts the activity of each OR into a combinatorial summary that records relative rankings of neuronal responses; we then construct the stimulus space based on these rankings. We found that the olfactory space constructed with our method has several desired properties: the space is consistent between individual mice, odorants from the same chemical classes are roughly clustered together, and the space cleanly captures the effect of changing odorant concentration.