  We study the 2D Ising model on three different types of lattices that are
topologically equivalent to spheres. The geometrical shapes are reminiscent of
the surface of a pillow, a 3D cube and a sphere, respectively. Systems of
volumes ranging up to O($10^5$) sites are simulated and finite size scaling is
analyzed. The partition function zeros and the values of various cumulants at
their respective peak positions are determined and they agree with the scaling
behavior expected from universality with the Onsager solution on the torus
($\nu=1$). For the pseudocritical values of the coupling we find significant
anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice
topology.
