A detailed analysis of the Riemann tensor in the neighbourhood of one bone and of the extrinsic curvature in the neighborhood of one triangular face in a simplicial geometry is presented. Unlike most previous analyses this analysis makes no reference to any particular choice of smoothing scheme. Explicit formulae will be presented for both the Riemann and extrinsic curvature tensors. These results are applied, using the formalism developed in an earlier paper, in deriving an exact formula for the integral extrinsic curvature. It is argued that for integrals of R2, R3, . . ., contributions must be expected from the legs, vertices, . . ., rather than just from the bones.