  The goal of this paper is to define a new class of objects which we call
triple groups and to relate them with Cherednik's double affine Hecke algebras.
This has as immediate consequences new descriptions of double affine Weyl and
Artin groups, the double affine Hecke algebras as well as the corresponding
elliptic objects. From the new descriptions we recover results of Cherednik on
automorphisms of double affine Hecke algebras.
