We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n≥7 can be obtained as a section of a (2+⌊n7⌋)-dimensional polytope with at most ⌈6n7⌉ vertices; and provides a geometric proof of the fact that every nonnegative n×m matrix of rank 3 has nonnegative rank not larger than ⌈6min(n,m)7⌉. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).
