I saw in this question that Mathematica can draw spherical triangles. I guess something similar can be done to plot a spherical polygon. I am interested in something similar:

I have a set of points on a sphere, as well as a set of edges connecting them (the edges are spherical geodesics). I would like to plot the corresponding partition, and to fill each spherical polygon with a different color. How can this be done?

Here is an example. The lines in the matrix $P$ are the coordinates of the points, the edges are represented in $E$ (indices represent points in the lines of $P$), and the faces are represented in $F$.

$$P = \begin{pmatrix} -0.9207 & -0.3896 & 0.0091 \\ -0.8272 & 0.5077 & -0.2399 \\ 0.2544 & -0.3511 & 0.9010 \\ 0.3510 & 0.6527 & 0.6712 \\ 0.5436 & -0.6326 & -0.5513 \\ 0.6016 & 0.2317 & -0.7643 \end{pmatrix}$$

$$ E = \begin{pmatrix} 1 & 2\\ 1 & 3 \\ 1 & 5 \\ 2 & 4 \\ 2 & 6 \\ 3 & 4\\ 3 & 5\\ 4 & 6\\ 5 & 6 \end{pmatrix}$$

$$ F = (1,3,5);(1,2,4,3);(1,2,6,5);(3,4,6,5);(2,4,6)$$

In the meantime, I found a Matlab solution using geom3d. Here is the output: