In crystal or molecular structures, multiple atoms may be equidistant from a central atom, especially in symmetric structures. These equidistant atoms are grouped to capture local geometric features and improve computational efficiency, while also ensuring that angle representations are unique and unaffected by the order of atoms within the same distance group. To accurately capture the angular relationships within each group, we calculate a squared mean of the angles between atoms in the group as the internal average angle of this group, introducing a nonlinearity that enhances the distinction between different angular arrangements compared to a simple average. We then calculate the central vector by summing the unit vectors of each atom in the group, ensuring that the resulting vector maintains rotational equivariance. In subsequent angle calculations, when two neighboring atoms belong to the same group, the internal average angle of that group is used. When only one neighboring atom belongs to a group, the central vector of that group is used to calculate the angle with the other atom. This approach reduces computational complexity and preserves the overall directional information, while also ensuring rotational invariance and uniqueness in the encoding. To capture all the possible bond angles, the number of neighboring atoms is set to 8.