2.26. What regular polygons can result from the intersection of a cube with a plane?
2.26. Each side of the obtained polygon belongs to one of the faces of the cube, so the number of its sides does not exceed 6. Moreover, sides belonging to opposite faces of the cube are parallel, since the lines of intersection of the plane with two parallel planes are parallel. Therefore, the section of the cube cannot be a regular pentagon, as it has no parallel sides. It is easy to check that a regular triangle, a square, and a regular hexagon can be sections of the cube.