In the Cage[1] isomer of the water hexamer, the free O-H bonds of the two end-cap water molecules can flip between "up'' (u) and "down'' (d) orientations, giving four conformers denoted uu, ud, du, and dd. Using the Moller-Plesset second order perturbation method and large basis sets, we calculate fully relaxed potential energy curves as a function of both u<->d torsional angles, denoted phi(1), phi(2). These predict du as the lowest conformer, with uu nearly degenerate and ud and dd at 30-40 and 50-70 cm(-1) higher energy, respectively. Along phi(1) the torsional barriers are about 200 cm(-1), along phi(2) between 80 and 110 cm(-1). The torsional zero-point energies are high, the vibrational ground states are strongly delocalized and averaging of the cluster properties is important along both phi(1) and phi(2). The dipole moment components vary strongly along both phi(1) and phi(2) : mu(a) changes from +0.8 to +2.2 D, mu(b) from +0.5 to +1.2 D, and mu(c) from 11.4 to -0.9 D. The phi(2) torsional fundamental of (H2O)(6) is predicted in the range 65-72 cm(-1) with an intensity of approximate to0.5 D-2, the phi(1) fundamental is in the 22-32 cm(-1) range, with an intensity of approximate to0.3 D-2. Both excitations are b/c hybrid perpendicular bands with a dominant b component. The torsional overtones should be very weak. (C) 2003 American Institute of Physics.