I noticed that Maya uses trapezoid (four sided) polygons. When triangulated (Polygons > Mesh > Triangulate) Maya simply splits each quad polygon into 4 sub triangles, like this:
![user added image](https://i263.photobucket.com/albums/ii133/TimmyEdwards/QuadTriSphere.png)
However I'm trying to achieve a different effect, one which staggers the triangles:
![user added image](https://i263.photobucket.com/albums/ii133/TimmyEdwards/NativeTriSphere.png)
The above was created in an obsolete rendering package for the Commodore Amiga (it's so old, it doesn't allow converting to 3DMax, Lightwave or Maya formats, and there are no third-party converters.)
I feel the latter is more elegant when you want to intentionally retain the polygonal 'facetted' appearance (for a crystal type effect), specifically the lovely helical/fibonacci-type spirals that make up the sphere. It also uses considerably fewer polygons than the non-staggered approach.
![user added image](https://i263.photobucket.com/albums/ii133/TimmyEdwards/Sphere.png)
Any easy way of doing this within Maya?