It can be solved with a piece of progarm, fortran, or matlab, etc.
Assume you have n border lines, i=1,n
On a xy plan, start from from the origin, x1=0, y1=0, draw the 1st line on x axis.
Because you know the length of the 1st border line, (x1,y1) can be calculated.
Start from (x1,y1), pick an angle, draw the 2nd line and calculate (x2,y2).
Start from (x2,y2), pick an angle, draw the 3rd line and calculate (x3,y3).
...... ......
Start from (xn-1,yn-1), pick an angle, draw the nth line and calculate (xn,yn).
Because this is a closed shape, (xn, yn) shall equal to (x1,y1), or the distance between
(xn,yn) and (x1,y1) shall be less than something to make an approximation.
Assume any angle can be picked from 1~359 with step of 1 degree, you should get a
solution with in 360^n calculations.
There may be more than one solutions. You can dry to start with different borders.
It seems interesting.