Determining a polytope by Radon partitions

Marilyn Breen

Vol. 43 (1972), No. 1, 27–37

DOI: 10.2140/pjm.1972.43.27

Abstract

In an extension of the classical Radon theorem, Hare and Kenelly have introduced the concept of a primitive partition, allowing a reduction to minimal subsets which still possess the necessary intersection property.

Here it is proved that primitive partitions in the vertex set P of a polytope reveal the subsets of P which give rise to faces of conv P, thus determining the combinatorial type of the polytope. Furthermore, the polytope may be reconstructed from various subcollections of the primitive partitions.

Mathematical Subject Classification

Primary: 52A25

Milestones

Received: 20 July 1971

Revised: 16 December 1971

Published: 1 October 1972