Regular Triangle Center

A Triangle Center is regular Iff there is a Triangle Center Function which is a Polynomial in $\Delta$, $a$, $b$, and $c$ (where $\Delta$ is the Area of the Triangle) such that the Trilinear Coordinates of the center are

$$f(a,b,c):f(b,c,a):f(c,a,b).$$

The Isogonal Conjugate of a regular center is a regular center. Furthermore, given two regular centers, any two of their Harmonic Conjugate Points are also regular centers.

See also Isogonal Conjugate, Triangle Center, Triangle Center Function