Polygons as Sections of Higher-Dimensional Polytopes

[摘要] We show that every heptagon is a section of a $3$-polytope with $6$ vertices. This implies that every $n$-gon with $n\geq 7$ can be obtained as a section of a $(2+\lfloor\frac{n}{7}\rfloor)$-dimensional polytope with at most $\lceil\frac{6n}{7}\rceil$ ver

[学科分类] 离散数学和组合数学

[关键词] polygon;polytope projections and sections;extension complexity;nonnegative rank;nonrealizability;pseudo-line arrangements