Abstract: Temporal knowledge graph embedding (TKGE) models are commonly utilized to infer the missing facts and facilitate reasoning and decision-making in temporal knowledge graph based systems. However, existing methods fuse temporal information into entities, potentially leading to the evolution of entity information and limiting the link prediction performance of TKG. Meanwhile, current TKGE models often lack the ability to simultaneously model important relation patterns and provide interpretability, which hinders their effectiveness and potential applications. To address these limitations, we propose a novel TKGE model which encodes \textbf{T}emporal knowledge graph \textbf{e}mbeddings via \textbf{A}rchimedean \textbf{S}piral \textbf{T}imeline (TeAST), which maps relations onto the corresponding Archimedean spiral timeline and transforms the quadruples completion to 3th-order tensor completion problem. Specifically, the Archimedean spiral timeline ensures that relations that occur simultaneously are placed on the same timeline, and all relations evolve over time. Meanwhile, we present a novel temporal spiral regularizer to make the spiral timeline orderly. In addition, we provide mathematical proofs to demonstrate the ability of TeAST to encode various relation patterns. Experimental results show that our proposed model significantly outperforms existing TKGE methods. Our code is available at {https://github.com/IMU-MachineLearningSXD/TeAST}.