The following example illustrates the technique for a facet representation of a sphere. The initial sphere has 4000 facets, on each iteration the number of polygons is reduced by 1000. If a smooth shaded rendering is being used then the model with 1000 facets is probably just as good as the original with 4 times the number of facets. As expected, for severe reductions in the number of polygons the surface undergoes a smoothing and loss of detail. This is readily illustrated for a gridded cube.
Careful consideration needs to be given to the edges of non-manifold surfaces.
A straightforward implementation will slowly eat away at the edge when the shortest facet edge is on the edge of the surface. And finally, applied to a model of the human cortex.