While the acoustic vowel space has been extensively studied in previous research, little is known about the high-dimensional articulatory space of vowels. The articulatory imaging techniques are limited to tracking only a few key articulators, leaving the rest of the articulators unmonitored. In the present study, we attempted to develop a detailed articulatory space obtained by training a 3D articulatory synthesizer to learn eleven British English vowels. An analysis-by-synthesis strategy was used to acoustically optimize vocal tract parameters that represent twenty articulatory dimensions. The results show that tongue height and retraction, larynx location and lip roundness are the most perceptually distinctive articulatory dimensions. Yet, even for these dimensions, there is a fair amount of articulatory overlap between vowels, unlike the fine-grained acoustic space. This method opens up the possibility of using modelling to investigate the link between speech production and perception.