My previous formulas were good but when I entered the numbers I was using a different calculator than normal and so my numbers are wrong. For a five sided blank with 1" segments the radius should be 0.6881in (~11/16") and the diameter should be 1.376in (~1 3/8").

The formula to calculate the outside diameter of a longitudinally segmented round piece is:

OD=X/tan(180/Y)

Where X is outside length of the segment after cutting the angles and Y is the number of segments.

One caveat, I have never actually done any segmenting, I just derived this mathematically and the formula may not work in all circumstances, although the only one where I can see that it won't work would be if you have to cut the inner part of the segment (the point of the triangle) off to get them to fit together.