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am1

Not too sure what it means by "The polygons containing each vertex make a single 'fan'? Does this just mean that it looks like the picture on the right?

Max

It's like the picture on the right - if you take all the polygons containing the vertex, you should be able to flatten them out into one planar shape.

Zhuoqian

This where I am confused. The vertices of the polygons should all lie within a same plane right? Because some mesh operations could cause vertices of a polygon to not lie within a same plane.