Potassium-ion batteries (KIBs) are a potential candidate to lithium-ion batteries (LIBs) but possess unsatisfactory capacity and rate properties.Herein,the metallic cobalt selenide quantum dots (Co0.85Se-QDs) encapsulated in mesoporous carbon matrix were designed via a direct hydrothermal method.Specifically,the cobalt selenide/carbon composite (Co0.85Se-QDs/C) possesses tertiary hierarchical structure,which is the primary quantum dots,the secondary petals flake,and the tertiary hollow micropolyhedron framework.Co0.85Se-QDs are homogenously embedded into the carbon petals flake,which constitute the hollow polyhedral framework.This unique structure can take the advantages of both nanoscale and microscale features:Co0.85Se-QDs can expand in a multidimensional and ductile carbon matrix and reduce the K-intercalation stress in particle dimensions;the micropetals can restrain the agglomeration of active materials and promote the transportation of potassium ion and electron.In addition,the hollow carbon framework buffers volume expansion,maintains the structural integrity,and increases the electronic conductivity.Benefiting from this tertiary hierarchical structure,outstanding K-storage performance (402 mAh g-1 after 100 cycles at 50 mA g-1) is obtained when Co0.85Se-QDs/C is used as KIBs anode.More importantly,the selenization process in this work is newly reported and can be generally extended to prepare other quantum dots encapsulated in edge-limited frameworks for excellent energy storage.