  We consider the problem of finding the ground state of a model type-II
superconductor on the two-dimensional surface of a sphere, penetrated by $N$
vortices. Numerical work shows the ground states to consist of a triangular
network of the vortices with twelve five-coordinated centres. Values of $N$ are
found with particularly low energy ground states, due to structures of high
symmetry. The large $N$ limit is treated within elasticity theory to compare
with the triangular vortex lattice that forms the ground state on an infinite
flat plane. Together with numerical work this demonstrates that the
thermodynamic limit $N\rightarrow\infty$ of the spherical system remains
different from the flat plane due to the presence of twelve disclination
defects.

Condensed Matter