Starting from a point cloud on the surface of a sphere, here is one way to create polylines, and faces between the points, using Meshlab.
The points could have been from the spherepoints script, or from antipodal, nonAntipodal, or electrostatic imported point file.

1. Create a comma delimited, or tab delimited text file, with the x, y, and z coordinates.
The file must have an extension of .asc. This can be done in MoI, by using the SavePointFile script to save spherical points in MoI, and typing the .asc extension.
If the point file already exists as a .txt delimited file, rename the file to .asc.

In windows, in order to enable the renaming of extensions, it is necessary to do the following:
Show or hide file name extensions (in windows)
A file name extension is a set of characters added to the end of a file name that determine which program should open it. Follow these steps to choose whether Windows displays these file extensions.
a. Open Folder Options by clicking the Start button , clicking Control Panel, clicking Appearance and Personalization, and then clicking Folder Options.
b. Click the View tab, and then, under Advanced settings, do one of the following:
○ To hide file extensions, select the Hide extensions for known file types check box, and then click OK.
○ To display file extensions, clear the Hide extensions for known file types check box, and then click OK.

Above paragraph Pasted from <http://windows.microsoft.com/en-US/windows-vista/Show-or-hide-file-name-extensions>

2. Open meshlab, and do File > Import Mesh, and select the *.asc file. Uncheck Grid triangulation.

3. Select Filters > Remeshing, simplification and reconstruction > Convex Hull Using the default entries, select Apply.

Note that nothing visible happens, unless, or until the wireframe icon has been selected.

4. Select: File > Export Mesh As > Alias Wavefront Object (*.OBJ) to save.
5. Use Michaels Obj23dmWireframe program to convert the *.obj file to *.3dm. (select one closed polyline for each face)
6. Open the *.3dm in MoI, select it, and use the Construct Planar command to form the faces.
There is a problem with reduced scale.
Color style is lost, unless the *.3dm is imported into MoI.

(Also tried out Filters > Surface Reconstruction: Ball Pivoting , but it may only partially work.)
(Have not tried out other point clouds.)