  We study the space of $C^1$ isogeometric spline functions defined on
trilinearly parameterized multi-patch volumes. Amongst others, we present a
general framework for the design of the $C^1$ isogeometric spline space and of
an associated basis, which is based on the two-patch construction [7], and
which works uniformly for any possible multi-patch configuration. The presented
method is demonstrated in more detail on the basis of a particular subclass of
trilinear multi-patch volumes, namely for the class of trilinearly
parameterized multi-patch volumes with exactly one inner edge. For this
specific subclass of trivariate multi-patch parameterizations, we further
numerically compute the dimension of the resulting $C^1$ isogeometric spline
space and use the constructed $C^1$ isogeometric basis functions to numerically
explore the approximation properties of the $C^1$ spline space by performing
$L^2$ approximation.
