  A first-order transition is numerically found in a spherical surface model
with skeletons, which are linked to each other at junctions. The shape of the
triangulated surfaces is maintained by skeletons, which have a one-dimensional
bending elasticity characterized by the bending rigidity $b$, and the surfaces
have no two-dimensional bending elasticity except at the junctions. The
surfaces swell and become spherical at large $b$ and collapse and crumple at
small $b$. These two phases are separated from each other by the first-order
transition. Although both of the surfaces and the skeleton are allowed to
self-intersect and, hence, phantom, our results indicate a possible phase
transition in biological or artificial membranes whose shape is maintained by
cytoskeletons.
