Slice one end (either blossom or stem end) off of your orange (photo 1)
Slice into your orange as if you’re going to cut a very thin slice, but stop about halfway through (photos 2 and 3)
Slice into the orange again (again, very thinly), but go all the way through (photo 4). You should have a slice of orange that has two thin pieces at the top half, but is solid on the bottom half (photo 5)
Make a slit in the centre of the solid half (photo 6)
Holding the orange on either side of the slit, twist and arrange on your platter, separating the top “petals” a bit (photos 7 and 8)