  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 angular
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 cluster
shapes. Using the observed X-ray isophotal axial ratio distribution for a
sample of galaxy clusters, we discuss intrinsic cluster shapes and, in
particular, if clusters can be described by axisymmetric models, such as oblate
and prolate ellipsoids. These models are currently favored when determining 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 rather than an oblate distribution. We address the possibility that
clusters are intrinsically triaxial by viewing triaxial ellipsoids at random
angles with the intrinsic axial ratios following an isotropic Gaussian
distribution. We discuss implications of our results on current attempts at
measuring the Hubble constant using galaxy clusters and suggest that an
unbiased estimate of the Hubble constant, not fundamentally limited by
projection effects, would eventually be possible with the SZ/X-ray method.
