14. All vertices of a regular polygon lie on the surface of a cube, but its plane does not coincide with any of the faces. What is the maximum number of vertices this polygon can have?
$\square \quad$ Omвem: 12 .

Assessment. It is clear that no more than 2 vertices of the polygon lie on each face, so there are no more than 12 vertices.

Example. Draw a section in the form of a regular hexagon through the midpoints of 6 edges. Inscribed in this hexagon, place a regular 12-sided polygon such that the sides of the 12-sided polygon alternate with the sides of the hexagon.

(A. Shapovalov)