Images observed at ground-based telescopes are blurred by Earth’s atmosphere. Adaptive optics systems can correct for this blurring by using a wavefront sensor to measure the instantaneous wavefront aberration created by the atmosphere, and a deformable mirror to apply correction to the aberrated wavefront. The European Extremely Large Telescope, one of the next generation of telescopes currently under construction, will have large supporting struts or arms (spiders) for the secondary mirror that obscure whole rows and columns of subapertures in the wavefront sensor. This phase discontinuity can allow large segment piston errors to arise between neighbouring segments, because the deformable mirror can produce the segment modes but the wavefront sensor senses them poorly. The spider for the EELT will have six arms, and we propose in this paper employing a six-sided prism for the wavefront sensor instead of the traditional four sided pyramid. We show that when the diffraction spikes from the spider arms are aligned in the middle of the prism faces, the sensitivty of the sensor, as measured by the sum of the singular values of the interaction matrix for the six segment piston modes, is 15% larger than if the diffraction spikes are aligned with the prism edges.