Minimum convex partitions of multidimensional polyhedrons

Abstract

In a normed space Rn over the field of real numbers ℜ, which is an α-space [26, 29], one derives the formula expressing the minimum number of d-convex pieces into which a geometric n-dimensional polyhedron can be partitioned. The mentioned problem has been kept unsolvable for more than 30 years. The special cases for R2 , R3 lead to nontrivial applications [19, 20, 23, 28, 30]. Mathematics Subject Classification: 68U05, 52A30, 57Q05

Keywords

• Geometric n-dimensional polyhedron
• d-convexity
• point of local non-d-convexity
• polyhedral complex
• oriented polytope
• dividing