The Polytope of m-Subspaces of a Finite Affine Space
Université Libre de Bruxelles, c.p. 216, Bd du Triomphe, 1050 Bruxelles, Belgium; firstname.lastname@example.org
Accepted: 21 December 2006
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.
Mathematics Subject Classification: 51A30 / 52B12 / 90C27
Key words: Convex polytope / finite affine space / m-subspace polytope
© EDP Sciences, ROADEF, SMAI, 2007