On the Cayley factorization of calotte conditions

Abstract

The calotte condition is the projective condition that a cycle of lines radiating from the vertices of a plane n-gon be the correct projection of a ring of faces surrounding an n-gonal piece of plane in space, the spatial figure being not entirely coplanar. This condition can be expressed as a homogeneous bracket polynomial. In general, this polynomial is not Cayley factorable. Henry Crapo conjectured that it becomes so when multiplied by a product of n-4 brackets. It is the purpose of this article to prove this conjecture. © 1994 Springer-Verlag New York Inc.