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Aug 22, 2017 at 10:56 comment added Joseph O'Rourke @Qurious: Allowing faces that are quads, pentagons, etc., doesn't change anything, because each quad could be partitioned into two triangles, each pentagon into three triangles, etc., and the number of vertices remains the same. So if you are minimizing vertices, it is appropriate to look at triangulations.
Aug 22, 2017 at 3:36 comment added Qurious Is it obvious that a triangulation will minimize the number of vertices of a genus g surface built of convex faces? In any case, thanks for the answer!
Aug 21, 2017 at 21:46 history edited Joseph O'Rourke CC BY-SA 3.0
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Aug 21, 2017 at 21:35 history answered Joseph O'Rourke CC BY-SA 3.0