Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and representational capacity. While existing ultra-low-bit methods rely on binary approximations or quantization-aware training(QAT), they often suffer from either limited representational capacity or huge training resource overhead. We introduce PTQ to Trit-Planes (PTQTP), a structured PTQ framework that decomposes weight matrices into dual ternary {-1, 0, 1} trit-planes. This approach achieves multiplication-free additive inference by decoupling weights into discrete topology (trit-planes) and continuous magnitude (scales), effectively enabling high-fidelity sparse approximation. PTQTP provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment without architectural modifications; and (3) uniform ternary operations that eliminate mixed-precision overhead. Comprehensive experiments on LLaMA3.x and Qwen3 (0.6B-70B) demonstrate that PTQTP significantly outperforms sub-4bit PTQ methods on both language reasoning tasks and mathematical reasoning as well as coding. PTQTP rivals the 1.58-bit QAT performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods, and the end-to-end inference speed achieves 4.63$\times$ faster than the FP16 baseline model, establishing a new and practical solution for efficient LLM deployment in resource-constrained environments. Code will available at https://github.com/HeXiao-55/PTQTP.