Can we reconstruct the entire internal shape of a room if all we can directly observe is a small portion of one internal wall, presumably through a window in the room? While conventional wisdom may indicate that this is not possible, motivated by recent work on 'looking around corners', we show that one can exploit light echoes to reconstruct the internal shape of hidden rooms. Existing techniques for looking around the corner using transient images model the hidden volume using voxels and try to explain the captured transient response as the sum of the transient responses obtained from individual voxels. Such a technique inherently suffers from challenges with regards to low signal to background ratios (SBR) and has difficulty scaling to larger volumes. In contrast, in this paper, we argue for using a plane-based model for the hidden surfaces. We demonstrate that such a plane-based model results in much higher SBR while simultaneously being amenable to larger spatial scales. We build an experimental prototype composed of a pulsed laser source and a single-photon avalanche detector (SPAD) that can achieve a time resolution of about 30ps and demonstrate high-fidelity reconstructions both of individual planes in a hidden volume and for reconstructing entire polygonal rooms composed of multiple planar walls.