I saw in [this question][1] 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][2]. Here is the output:

![enter image description here][3]


  [1]: http://mathematica.stackexchange.com/questions/23053/triangle-mapped-on-a-sphere-in-mathbb-r3
  [2]: http://www.mathworks.com/matlabcentral/fileexchange/24484-geom3d
  [3]: https://i.sstatic.net/ywMIR.gif