Metastable beta-As2Te3 (R (3) over barm, a = 4.047 angstrom and c = 29.492 angstrom at 300 K) is isostructural to layered Bi2Te3 and is known for similarly displaying good thermoelectric properties around 400 K. Crystallizing glassy-As2Te3 leads to multiphase samples, while beta-As2Te3 could indeed be synthesized with good phase purity (97%) by melt quenching. As expected, beta-As2Te3 reconstructively transforms into stable alpha-As2Te3 (C2/m, a = 14.337 angstrom, b = 4.015 angstrom, c = 9.887 angstrom, and beta = 95.06 degrees) at 480 K. This beta -> alpha transformation can be seen as the displacement of part of the As atoms from their As2Te3 layers into the van der Waals bonding interspace. Upon cooling, beta-As2Te3 displacively transforms in two steps below T-S1 = 205-210 K and T-S2 = 193-197 K into a new beta'-As2Te3 allotrope. These reversible and first-order phase transitions give rise to anomalies in the resistance and in the calorimetry measurements. The new monoclinic beta'-As2Te3 crystal structure (P2(1)/m, a = 6.982 angstrom, b = 16.187 angstrom, c = 10.232 angstrom, beta = 103.46 degrees at 20 K) was solved from Rietveld refinements of X-ray and neutron powder patterns collected at low temperatures. These analyses showed that the distortion undergone by beta-As2Te3 is accompanied by a 4-fold modulation along its b axis. In agreement with our experimental results, electronic structure calculations indicate that all three structures are semiconducting with the alpha-phase being the most stable one and the beta'-phase being more stable than the beta-phase. These calculations also confirm the occurrence of a van der Waals interspace between covalently bonded As2Te3 layers in all three structures.