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The Beijing Spectrometer III (BESIII) superconducting solenoid magnet, which is running in the Beijing Electron Positron Collider II (BEPC-II), is an important part of BESIII and provides a 1 Tesla field in the main drift chamber. A 3-D mapping device with three 3-D probes was fabricated to measure the field components of Bz, Br and BΦ. The mapping of the magnetic field of the BESIII superconducting solenoid magnet is presented, with the accelerator interaction region magnets located inside the BESIII solenoid excited to different current values. A set of polynomials, and a few trigonometric-Bessel terms are used to fit the data. The measurements and the functional model agree to 5 Gauss within the main drift chamber tracking volume at nominal field values. [ABSTRACT FROM AUTHOR]