J. Heinonen et A. Hinkkanen, QUASI-CONFORMAL MAPS BETWEEN COMPACT POLYHEDRA ARE QUASI-SYMMETRIC, Indiana University mathematics journal, 45(4), 1996, pp. 997-1019
It is proved that quasiconformal homeomorphisms, defined via an infini
tesimal pointwise condition, between compact polyhedra are quasisymmet
ric, that is, they satisfy a global distortion condition, provided the
polyhedra in question have no one dimensional parts.