Defined as squares are open-air spaces for public use, the position of which is dictated by the network of streets as they are located at their junction, while their density is determined by taking possibly into account demographic needs.

At Poliochne there are two central paved squares, Square 103 at about the centre of the settlement, and Square 106 to the north of it. The linear urban plan and the narrow streets between the insulae and/or other factors imposed their position in the eastern sector of the settlement, at the junction of the main thoroughfare 105 with the central street 102 and the side street 124 in the first case, and of the same thoroughfare with side street 111 in the second. In both squares there are wells that are eight or more metres deep.

Square 103, at the triple junction of streets 102-105-124, preserves an extensive pavement of monolithic flagstones of impressive size. Its position, at about the centre of the settlement, at the meeting point of three streets and with open access all around it, enhances the square as a nodal point in the settlement. It could function as a venue of assembly and decision-making, right outside one of the most opulent buildings of the final phase of the settlement, Building A of Insula VIII with Megaron 605. The square was larger at first but it was gradually encroached on by additions to the existing buildings of insulae VIII and ΙΧ, as well as by new constructions, until it was confined to around its well, which had been sunk in its west part.

The well in the square remained unaltered. It is stone-lined with parallelepiped blocks in courses reminiscent of isodomic masonry. The shaft, 7.70 m deep without reaching the bottom, is of perfect circular cross-section with internal diameter 1.63 m and absolutely straight; only the wellhead is of pentagonal form. During the Second World War, explosives and other munitions were thrown into the well by the German troops, who brazenly violated the monument.

A stone-built drain, the top of which is at the height of the mouth of the well in the square and in contact with its walls, follows the downward slope of the ground (N→S and E→W) and carries off water from the perimeter of the square, the well and the neighbouring insulae VIII and ΙΧ via the adjacent streets. It may well have functioned also as an overflow channel of the well, at the same time distributing water to the rest of the settlement. Moreover, it is possible that the drainage channel of Building A in Insula VIII also terminated at the well. If these hypotheses are valid, this reinforces the possibility that the settlement at Poliochne had a more complex network of water management than was previously thought, already from the late third millennium BC. In any case, the paving at this point, as also at the central entrance of the settlement, where too there is a steep gradient of the ground, seems to serve a practical purpose, namely to prevent erosion of the street surfaces by rainwater rushing through the settlement from east to west and north to south. The torrential flow would have been stemmed also by the stone-built storm drain to the west of street 105 and slightly north of the point where the paving of the square is preserved.