 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 129, Number 7, Pages 21032109
S 00029939(00)057282
Article electronically published on November 21, 2000
PROJECTIONS OF POLYTOPES ON THE PLANE
AND THE GENERALIZED BAUES PROBLEM
CHRISTOS A. ATHANASIADIS
(Communicated by John R. Stembridge)
Abstract. Given an affine projection : P Q of a dpolytope P onto a
polygon Q, it is proved that the poset of proper polytopal subdivisions of Q
which are induced by has the homotopy type of a sphere of dimension d  3
if maps all vertices of P into the boundary of Q. This result, originally
conjectured by Reiner, is an analogue of a result of Billera, Kapranov and
Sturmfels on cellular strings on polytopes and explains the significance of the
interior point of Q present in the counterexample to their generalized Baues
conjecture, constructed by Rambau and Ziegler.
1. Introduction
Motivated by their theory of fiber polytopes [6] and [18, Lecture 9], Billera and
Sturmfels have associated to any affine projection of convex polytopes : P Q
