It is not possible if the two geometric figures are finite.
A Circle.
a polygon a polygon * * * * * No it is not! If the line is in that plane then it is the whole line. If not, it is a single point.
F is not a geometric shape that is used. The standard geometric term vertex means the intersection point of two sides of a plane figure. If F is meant to represent figure this term might apply.
a plane
It is the cross-section of the figure by the plane.
That thing.
Cross Section
the figure defined by intersection of a cone and a plane.
the figure defined by intersection of a cone and a plane.
cross section
A dodecagon is a plane geometric figure. It is not capable of doing anything!
A triangle quadrilateral is an oxymoron. It is a three sided plane figure with four sides. Even if such a figure were possible, it would be merely a geometric shape: not capable of doing anything!