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Quarter Plates?

I found this trying to overcome my quarter plate issue with the 9x9 Go board. The slight bowing you see is nonexistent with ample side support (1x2, 2x2 bricks, etc). I am not sure the hinge tops are quite quarter plates, but I am sure the raised lettering on these parts isn't helping.

 

I tried using some plates, tiles, and flags to determine the actual fraction of a plate, but when I broke out the calipers I found that the plates, tiles, and flags I was using were not quite the dimensions I expected, so I just took a sample of 32 hinge tops and with statistics concluded the actual fraction is about 5/16 of a plate.

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Uploaded on January 13, 2015