Estimating the 6D pose of an object from a single RGB image is a critical task that becomes additionally challenging when dealing with symmetric objects. Recent approaches typically establish one-to-one correspondences between image pixels and 3D object surface vertices. However, the utilization of one-to-one correspondences introduces ambiguity for symmetric objects. To address this, we propose SymCode, a symmetry-aware surface encoding that encodes the object surface vertices based on one-to-many correspondences, eliminating the problem of one-to-one correspondence ambiguity. We also introduce SymNet, a fast end-to-end network that directly regresses the 6D pose parameters without solving a PnP problem. We demonstrate faster runtime and comparable accuracy achieved by our method on the T-LESS and IC-BIN benchmarks of mostly symmetric objects. The code is available at https://github.com/lyltc1/SymNet.