  We show that much of the theory of finite tight frames can be generalised to
vector spaces over the quaternions. This includes the variational
characterisation, group frames, and the characterisations of projective and
unitary equivalence. We are particularly interested in sets of equiangular
lines (equi-isoclinic subspaces) and the groups associated with them, and how
to move them between the spaces $\Rd$, $\Cd$ and $\Hd$. We present and discuss
the analogue of Zauner's conjecture for equiangular lines in $\Hd$.
