Help with Duplo umbrella 40554

[Rene Rechthaler]

At this point it is possible to choose the angle of the axis versus the ridges/ribs. The current shape doesn't have a line of points at either red or blue angles. The smoothness of the shape at both angles requires that the lines of points are symmetrically on both sides of the angle. To make it worse, the spacing is different at these two angles. All of this makes the current shape unsuitable for placement with only cardinal rotations where every other segment is forward and every other in reverse. If only cardinal rotations are permitted (i.e. if 45 degree rotations wouldn't be), then the subfile should cover one quarter of the shape so that the angle offset at the borders are the same. Looking at this particular shape, which angle would you choose for the axis and which arch length would you choose for the subfile?

why no vertices exactly on the peak? it can still be a (round) curve (like a cyl prim)...
then it would be possible to use 1 subpart (each 45°) 8 times, without rotations...
   
red - main axis cut lines
blue - diagonal cut
yellow - scaling direction

Edit: theoretically, even a 1/16 cut would be possible (the rotated ones along the blue 45° curve need a high enough precision for that)