  Using Monte Carlo techniques, the critical Binder cumulant U* of isotropic
nearest-neighbour Ising models on square and triangular lattices is studied.
For rectangular shapes, employing periodic boundary conditions, U* is found to
show the same dependence on the aspect ratio for both lattice types. Similarly,
applying free boundary conditions for systems with square as well as circular
shapes for both lattices, the simulational findings are also consistent with
the suggestion that, for isotropic Ising models with short-range interactions,
U* depends on the shape and the boundary condition, but not on the lattice
structure.
