Is it true that if s and t are simplices with dimension dim(s) and dim(t) respectively, such that Star(s) and Star(t) have isomorphic subdivisions, then Star(f) and Star(g) also have isomorphic subdivisions, where f is a face of s with dim(f) = dim(s) - 1 and g is a simplex in a suitable simplicial complex with dim(g) = dim(t) - 1 ??? In short, if star of 2 simplices are homeomorphic, is it true that star of their faces are also homeomorphic?