I first read about this way to sculpt an orange in The Art of Astonishment (vol 1) by the magician Paul Harris. However the diagrams in the book are wrong.
First draw an equator around the orange. I’ve found a biro works well. Then draw 8 equally spaced vertical lines alternating above and below the equator. See the second photo. The lines stop about 2cm from the poles.
Now make a cut through the peel on each of the vertical lines. Then make two parallel cuts (to the left and right) of those vertical lines. This creates two strips of peel that are about 0.5 cm thick. You’ve now made 24 cuts.
This is the slightly tricky bit… from the top extend one of the righthand cuts in an arc to the lefthand cut of the next bank of 3 cuts in the same hemisphere. Now extend the central cut in an arc to the next central cut. You’ll create a loop 0.5 cm wide. Repeat this process 4 times on the top hemisphere and it will look like photo 3.
Now turn the orange upside down and repeat the cuts for the other hemisphere. Photo 4.
The final cuts are along the equator but these are deep so they divide the orange into 2 hemispheres. Don’t cut through the strips. Then gently pull the two halves apart. It helps to pull the cut loops away from the orange before separating. You’ll end up with something looking like first photo at the top of this post.