The paper explores the compensation behaviors and phase transitions of a new 3D fullerene-like polymer using the Monte Carlo (MC) method. The authors present the ground-state phase diagrams and magnetization profiles, identifying the conditions for the occurrence of the compensation temperature \( T_{comp} \). They classify the magnetization curves into N-type and P-type according to Néel theory. The study also examines how physical parameters affect the transition temperature \( T_C \) and the compensation temperature \( T_{comp} \) through phase diagrams. Critical exponents of the system are calculated and compared with existing results, showing good agreement. Additionally, the paper discovers triple hysteresis loops. The research builds on previous studies of fullerene-like structures and aims to provide insights into the magnetic properties of 3D fullerene-like polymers, which have attracted significant attention due to their unique physical properties.The paper explores the compensation behaviors and phase transitions of a new 3D fullerene-like polymer using the Monte Carlo (MC) method. The authors present the ground-state phase diagrams and magnetization profiles, identifying the conditions for the occurrence of the compensation temperature \( T_{comp} \). They classify the magnetization curves into N-type and P-type according to Néel theory. The study also examines how physical parameters affect the transition temperature \( T_C \) and the compensation temperature \( T_{comp} \) through phase diagrams. Critical exponents of the system are calculated and compared with existing results, showing good agreement. Additionally, the paper discovers triple hysteresis loops. The research builds on previous studies of fullerene-like structures and aims to provide insights into the magnetic properties of 3D fullerene-like polymers, which have attracted significant attention due to their unique physical properties.