Reconfigurable intelligent surfaces (RISs) are expected to be a main component of future 6G networks, due to their capability to create a controllable wireless environment, and achieve extended coverage and improved localization accuracy. In this paper, we present a novel cooperative positioning use case of the RIS in mmWave frequencies, and show that in the presence of RIS, together with sidelink communications, localization with zero access points (APs) is possible. We show that multiple (at least three) half-duplex single-antenna user equipments (UEs) can cooperatively estimate their positions through device-to-device communications with a single RIS as an anchor without the need for any APs. We start by formulating a three-dimensional positioning problem with Cram\'er-Rao lower bound (CRLB) derived for performance analysis. After that, we discuss the RIS profile design and the power allocation strategy between the UEs. Then, we propose low-complexity estimators for estimating the channel parameters and UEs' positions. Finally, we evaluate the performance of the proposed estimators and RIS profiles in the considered scenario via extensive simulations and show that sub-meter level positioning accuracy can be achieved under multi-path propagation.