  We use absolute trigonometric parallaxes from the Hipparcos Catalogue to
determine individual distances to members of the Hyades cluster, from which the
3-dimensional structure of the cluster can be derived. Inertially-referenced
proper motions are used to rediscuss distance determinations based on
convergent-point analyses. A combination of parallaxes and proper motions from
Hipparcos, and radial velocities from ground-based observations, are used to
determine the position and velocity components of candidate members with
respect to the cluster centre, providing new information on cluster membership:
13 new candidate members within 20 pc of the cluster centre have been
identified. Farther from the cluster centre there is a gradual merging between
certain cluster members and field stars, both spatially and kinematically.
Within the cluster, the kinematical structure is fully consistent with parallel
space motion of the component stars with an internal velocity dispersion of
about 0.3 km/s. The spatial structure and mass segregation are consistent with
N-body simulation results, without the need to invoke expansion, contraction,
rotation, or other significant perturbations of the cluster. The quality of the
individual distance determinations permits the cluster zero-age main sequence
to be accurately modelled. The helium abundance for the cluster is determined
to be Y=0.26+/-0.02 which, combined with isochrone modelling including
convective overshooting, yields a cluster age of 625+/-50 Myr. The distance to
the observed centre of mass is 46.34+/-0.27 pc, corresponding to a distance
modulus m-M=3.33+/-0.01 mag for the objects within 10 pc of the cluster centre
(roughly corresponding to the tidal radius). Discrepancies with previous
distance estimates are investigated and explained.
