Neutron scattering studies on powder and single crystals have provided new evidence for unconventional magnetism in Cu2Te2O5Cl2. The compound is built from tetrahedral clusters of S=1/2 Cu2+ spins located on a tetragonal lattice. Magnetic ordering, emerging at T-N=18.2 K, leads to a very complex multi-domain, most likely degenerate, ground state, which is characterized by an incommensurate (ICM) wave vector k similar to[0.15,0.42,1/2]. The Cu2+ ions carry a magnetic moment of 0.67(1)mu(B)/Cu2+ at 1.5 K and form a four-helix spin arrangement with two canted pairs within the tetrahedra. A domain redistribution is observed when a magnetic field is applied in the tetragonal plane (H(c)approximate to 0.5 T), but not for H parallel to c up to 4 T. The excitation spectrum is characterized by two well-defined modes, one completely dispersionless at 6 meV, the other strongly dispersing to a gap of 2 meV. The reason for such complex ground state and spin excitations may be geometrical frustration of the Cu2+ spins within the tetrahedra, intra- and inter-tetrahedral couplings having similar strengths and strong Dzyaloshinski-Moriya anisotropy. Candidates for the dominant intra- and inter-tetrahedral interactions are proposed.