jMonkeyEngine does not have a program to create meshes graphically. There are many mesh programs. The one that is used most often is Blender. There are many books and tutorials on using Blender.
You can get Blender from blender.org.
After successfully installing the program, you have to include a add-on to Blender. You can get the zip file from this site.
Extract the python file indicated to addons folder. You should search for addons folder to see where your actual folder is located.
Next, in Blender you can open User Preferences from the File menu, select Addons tab and Import/Export section. The ORGE Exporter should be there and should be unchecked. Check it to enable it.
When Blender is opened, there should be a cube, in its default setup, and it should be selected. Press x to delete it, and confirm with click. Next, use the Add menu, and create the Mesh and Icosphere.
Next the Icosphere is exported using Export option in the File menu. You should create a folder, and in Export options, select that folder.
The file Icoshpere.mesh.xml is created. It is a text file and can be opened in any text processor. From that file, you can see there are 240 vertices. The actual number of physical vertices is less than 240. Further, we have 80 faces. Each face is a triangle, and the corresponding 3 vertices, for each face, are listed at the end of xml file.
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