Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Show Planes
SYMMETRYGENERATOR_DRAWParameter: Type
SYMMETRYGENERATOR_TYPEParameter: X
SYMMETRYGENERATOR_PLANAR_AXIS_XParameter: Y
SYMMETRYGENERATOR_PLANAR_AXIS_YParameter: Z
SYMMETRYGENERATOR_PLANAR_AXIS_ZParameter: Axis
SYMMETRYGENERATOR_RADIAL_AXISParameter: Rotation Offset
SYMMETRYGENERATOR_RADIAL_ROTATIONOFFSETParameter: Source Slice
SYMMETRYGENERATOR_RADIAL_SOURCESLICEParameter: Slice Count
SYMMETRYGENERATOR_RADIAL_SLICECOUNTParameter: Mirror
SYMMETRYGENERATOR_RADIAL_MIRRORParameter: Keep Parametric
SYMMETRYGENERATOR_KEEPHIERARCHYParameter: Weld
SYMMETRYGENERATOR_WELDParameter: Cut Along Plane
SYMMETRYGENERATOR_CUTALONGPLANEParameter: Remove Outside
SYMMETRYGENERATOR_REMOVEOUTSIDEParameter: Tolerance
SYMMETRYGENERATOR_TOLERANCEParameter: Snap Points to Plane
SYMMETRYGENERATOR_SNAPTOPLANEParameter: Copy to Hub
SYMMETRYGENERATOR_COPYTOHUBParameter: Paste from Hub
SYMMETRYGENERATOR_COPYFROMHUB