The convex hulls of the vertices of a polygon of order n

Douglas Derry

Vol. 38 (1971), No. 3, 583–596

DOI: 10.2140/pjm.1971.38.583

Abstract

Let π_n : A₁A₂⋯A_r be a polygon of real order n in real projective n-space L_n,r ≧ n + 3, with the vertices A_t.,A₂,⋯ , A_r. If H_n−1 be a hyperplane for which A_i∉H_n−1,1 ≦ i ≦ r, let H(π_n) be the convex full of the set {A₁,A₂,⋯,A_r} defined in the affine space L_n∖H_n−1. This paper gives a classification of the combinatorial types of the sets H(π_n) for a fixed π_n.

Mathematical Subject Classification

Primary: 52A25

Milestones

Received: 10 October 1970

Published: 1 September 1971