Details

A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.

Reference

[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Sep 7, 2022) faculty.evansville.edu/ck6/encyclopedia.