THE ORDER DIMENSION OF CONVEX POLYTOPES

Authors
BRIGHTWELL G TROTTER WT
Citation
G. Brightwell et Wt. Trotter, THE ORDER DIMENSION OF CONVEX POLYTOPES, SIAM journal on discrete mathematics, 6(2), 1993, pp. 230-245
Citations number
17
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on discrete mathematics → ACNP
ISSN journal
08954801
Volume
6
Issue
2
Year of publication
1993
Pages
230 - 245
Database
ISI
SICI code
0895-4801(1993)6:2<230:TODOCP>2.0.ZU;2-W
Abstract
With a convex polytope M in R3, a partially ordered set P(M) is associ ated whose elements are the vertices, edges, and faces of M ordered by inclusion. This paper shows that the order dimension of P(M) is exact ly 4 for every convex polytope M. In fact, the subposet of P(M) determ ined by the vertices and faces is critical in the sense that deleting any element leaves a poset of dimension 3.