= Incenter of a tetrahedron
{title2=$I=(S_AA+S_BB+S_CC+S_DD)/(S_A+S_B+S_C+S_D)$}
= Incentre of a tetrahedron
{synonym}
The center of the sphere tangent to all four faces is the positive face-area-weighted combination of the opposite vertices. If $V$ is the <volume> and $S$ the total face area, its distance from each face is $3V/S$. Indeed its weight for vertex $A$ is $S_A/S$ and the corresponding altitude is $3V/S_A$, so their product is the common distance. Positive weights place it inside the <tetrahedron>.
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