Simplicial Brill wave initial data

Regge calculus is used to construct initial data for vacuum axisymmetric Brill waves at a moment of time symmetry. We argue that only a tetrahedral lattice can successfully reproduce the continuum solution, and develop a simplicial axisymmetric lattice based on the co-ordinate structure of the continuum metric. This is used to construct initial data for Brill waves in an otherwise flat spacetime, and for the distorted black hole spacetime of Bernstein. These initial data sets are shown to be second order accurate approximations to the corresponding continuum solutions.