Hope doing well and being healthy. I have a basic question on centroid of tetrahedrons.
Are the coordinate of the centroid always the averages of $x$ and $y$ and $z$, by which I mean $$\frac14(x_1+x_2+x_3+x_4),\quad\frac14(y_1+y_2+y_3+y_4),\quad\frac14(z_1+z_2+z_3+z_4)$$
(For example, MBD Alchemie's YouTube video "Centroid of a Tetrahedron" shows it.)
I always see that people consider a $3:1$ ratio. Is it valid for all the tetrahedrons? I mean in case of having very flat tetrahedrons with enequal side tangles, can the centroid be calculated using this simple equation? To make my request a more clear, I have uploaded a photo of an irregular tetrahedron here:
In advance, I do appreciate any response.