SOLUTIONS OF THE REGGE EQUATIONS ON SOME TRIANGULATIONS OF CP2

Simplicial geometries are collections of simplices making up a manifol d together with an assignment of lengths to the edges that define a me tric on that manifold. The simplicial analogs of the Einstein equation s are the Regge equations. Solutions to these equations define the sem iclassical approximation to simplicial approximations to a sum over ge ometries in quantum gravity. In this paper, we consider solutions to t he Regge equations with a cosmological constant that give Euclidean me trics of high symmetry on a family of triangulations of CP2 presented by Banchoff and Kuhnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a s olution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calc ulus. (C) 1997 American Institute of Physics.