  We have studied two types of meshwork models by using the canonical Monte
Carlo simulation technique. The first meshwork model has elastic junctions,
which are composed of vertices, bonds, and triangles, while the second model
has rigid junctions, which are hexagonal (or pentagonal) rigid plates.
Two-dimensional elasticity is assumed only at the elastic junctions in the
first model, and no two-dimensional bending elasticity is assumed in the second
model. Both of the meshworks are of spherical topology. We find that both
models undergo a first-order collapsing transition between the smooth spherical
phase and the collapsed phase. The Hausdorff dimension of the smooth phase is
H\simeq 2 in both models as expected. It is also found that H\simeq 2 in the
collapsed phase of the second model, and that H is relatively larger than 2 in
the collapsed phase of the first model, but it remains in the physical bound,
i.e., H<3. Moreover, the first model undergoes a discontinuous surface
fluctuation transition at the same transition point as that of the collapsing
transition, while the second model undergoes a continuous transition of surface
fluctuation. This indicates that the phase structure of the meshwork model is
weakly dependent on the elasticity at the junctions.
