Step 3: Crack it Open
Place your thumbs inside the cut flower end, with the pads of your thumbs pressing against opposing segments of the pomegranate. Pull apart gently but firmly, and the pomegranate will crack open along the lines you've scored in the skin, and the internal segments will separate along their natural boundaries.
Adjust your grip to separate each segment along the scored lines. The end result is shown below - you'll have as many side segments as you did ribs/flats, plus a central cone-shaped chunk associated with the stem end.
Notice the almost complete lack of messy pomegranate juice! Just one drop on the plate, the result of squeezing a bit too roughly and popping one seed.