Task-dependent changes in the shape and thickness of Listing's plane

We examined the 2D surface formed by 3D eye positions of normal subjects to determine whether the shape and thickness changed in tasks that differed in saccadic directions; random, horizontal, vertical, radial, clockwise and counter-clockwise. Eye positions during the random task did not lie precisely on Listing's plane but on a surface with a small twist. This twist was present before, during, and after saccades. The degree of twist changed with the task; becoming less twisted for horizontal tasks and more twisted in the vertical tasks. The surface thickness changed with the task becoming thicker for multidirectional tasks. This greater thickness may occur because surfaces obtained in multidirectional tasks are the composite of surfaces with slightly different shapes.