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Please help with this cylinder curve problem.

KoolKat
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The problem that I am having is where the rectangle-shape comes into the side of the cylinder; that face-area of the side of the cylinder doesn’t curve like the rest of the sides of the cylinder; it basically sticks out when I put it into smooth preview.  This is one object by the way.

 

My images show the four corners that create the hole that the rectangle goes through are connected with an EDGE to the four corners of the side-face of the cylinder I am having a problem with, which creates a five star pole for each corner by the way.  With that said, one attempt I tried that failed was I moved the EDGES from each of those four corners of the side-face of the cylinder and had them connect to the two edge loops that I added around the side of the cylinder, which is not in any of the images.  If any of that made any sense.  It failed anyways.

 

I would greatly appreciate any help.    

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