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Articulatory inversion is the problem of recovering the sequence of vocal tract shapes that produce a given acoustic speech signal. Traditionally, its difficulty has been attributed to nonuniqueness of the inverse mapping, where different vocal tract shapes can produce the same acoustics. However, evidence for the nonuniqueness has been restricted to theoretical studies, or to data from atypical speech or very specific sounds. We present a systematic large-scale study using articulatory data for normal speech from the Wisconsin XRDB. We find that nonuniqueness does exist for some sounds, but that the majority of normal speech is produced with a unique vocal tract shape.