Galaxy clusters: oblate or prolate?

It is now well known that a combined analysis of the Sunyaev-Zel'dovich (SZ ) effect and the X-ray emission observations can be used to determine the a ngular diameter distance to galaxy clusters, from which the Hubble constant is derived. Given that the SZ/X-ray Hubble constant is determined through a geometrical description of clusters, the accuracy to which such distance measurements can be made depends on how well one can describe intrinsic clu ster shapes. Using the observed X-ray isophotal axial ratio distribution fo r a sample of galaxy clusters, we discuss intrinsic cluster shapes and, in particular, if clusters can be described by axisymmetric models, such as ob late and prolate ellipsoids. These models are currently favoured when deter mining the SZ/X-ray Hubble constant. We show that the current observational data on the asphericity of galaxy clusters suggest that clusters are more consistent with a prolate than with an oblate distribution. We address the possibility that clusters are intrinsically triaxial by viewing triaxial el lipsoids at random angles with the intrinsic axial ratios following an isot ropic Gaussian distribution. We discuss implications of our results on curr ent attempts at measuring the Hubble constant using galaxy clusters and sug gest that an unbiased estimate of the Hubble constant, not fundamentally li mited by projection effects, would eventually be possible with the SZ/X-ray method.