Recent works on reconstruction of room geometry from echoes assume that the geometry of the sensor array is known. In this paper, we show that such an assumption is not essential; echoes provide sufficient clues to reconstruct the room’s and the array’s geometries jointly, even from a single acoustic event. Rather than focusing on the combinatorial problem of matching the walls and the recorded echoes, we provide algorithms for solving the joint estimation problem in practical cases when this matching is known and the number of microphones is small. We then explore intriguing connections between this problem and simultaneous localization and mapping (SLAM), and show that SLAM can be solved by the same methods. Finally, we demonstrate how effective the proposed methods are by numerical simulations and experiments with real measured room impulse responses.