We present a tomographic reconstruction of polar plumes as observed in the Extreme Ultraviolet in January 2010. Plumes are elusive structures visible in polar coronal holes that may play an important role in the acceleration of the solar wind. However, despite numerous observations, little is irrefutably known about them. Because of line of sight effects, even their geometry is subject to debate. Are they genuine cylindrical features of the corona or are they only chance alignments along the line of sight? Tomography provides a means to reconstruct the volume of an optically thin object from a set of observations taken from different vantage points. In the case of the Sun, these are typically obtained by using a solar rotation worth of images, which limits the ability to reconstruct short lived structures. We present here a tomographic inversion of the solar corona obtained using only 6 days of data. This is achieved by using simultaneously three space telescopes (EUVI/STEREO and SWAP/PROBA2) in a very specific orbital configuration. The result is the shortest possible tomographic snapshot of polar plumes. The 3D reconstruction shows both quasi-cylindrical plumes and a network pattern that can mimic them by line of sight superimpositions. This suggests that the controversy on plume geometry is due to the coexistence of both types of structures.