A bit of both.
It was clearly a hipotrochoid by first glance.
Then, if you look at the number of repeats, there are ten loops before the small circle inside reaches it's starting point.
That means it's circumference is one tenth of the larger circle, meaning r=R/10.
D could be find for any spirograms with that r/R ration, to result in such overlapping.
If d=r, there would be spikes at the side, touching the outer ring, for the loops it should be larger.
Once the shape was right, all parametres was scaled accordingly to the overall size.
Which this case was 2R-2r+2d=1,8R+2d for width and height.
Speaking of calculation, from the shape and width of the object,
1,8R+2d=126;
and the diametre of the inner hole
2R-2r-2D=1,8R+2d=18.
Now that could be calculated:
1,8R+2d=126
1,8R-2d=18
______________
1,8R+2d-(1,8R-2d)=126-18
4d=108
d=27
1,8R+2*27=126
R=(126-2*27)/1,8=72/1,8=40
r=0,1R=4
Shame on me, no try and error would have been necessary.