The searchmight toolbox was developed by Francisco Pereira and the Botvinick Lab and introduced in Information mapping with pattern classifiers. The toolbox is specialized for searchlight analysis, streamlining and speeding the process of trying different classification algorithms on the same datasets.
Francisco said that, by default, the toolbox uses cubical searchlights (other shapes can be manually defined). In the image of different one-voxel radius searchlights, this is the one that I labeled "edge, face, or corner": 26 surrounding voxels for a one-voxel radius searchlight. Larger radii are also cubes.
Pereira, Francisco, & Botvinick, Matthew (2011). Information mapping with pattern classifiers: A comparative study. NeuroImage. DOI: 10.1016/j.neuroimage.2010.05.026