Understanding the geometry of indoor space is essential for constructing realistic digital twins for metaverse applications and for realizing an intelligent audio system that adaptively renders spatial audio according to the room condition. We propose Echo-Vision Network (EV-Net) that reveals the complex shape of a room through high-level inference on acoustic echoes. Despite the attempts for estimating room shapes using vision and sound data, conventional methods have intrinsic limitations in that non-line-of-sight (NLOS) regions invisible from the camera or audio device position cannot be estimated. Moreover, vision-based approaches are unable to reliably identify walls with glass or black body materials. To overcome these limitations, our proposed EV-Net leverages the relation between high-order reflections of room impulse responses (RIRs) that can be easily measured from a single off-the-shelf voice assistant speaker. An efficient encoder-decoder architecture with a multi-aggregation module is designed to efficiently encodes geometry-related features from complex RIRs. The performance of the proposed method and its ability to exploit high-order reflections are demonstrated through a large room dataset with RIRs from various shapes of rooms including non-convex rooms with NLOS walls. Its robustness to various perturbations possible in real-world environments is also tested and verified by noisy RIR datasets simulated for different noise levels and room temperatures.