While you would typically use a knife to score the skin of a pomegranate, you can make the same shallow cuts necessary to open the fruit by other means if you don't have access to a knife. In fact, any instrument with a narrow edge will do in a pinch, from a nail file to a sharp stick to long fingernails if you have them. A large bowl makes opening the pomegranate less messy, but you can make do with a large paper bag or towel spread on your work surface. The sweet-tart and juicy seeds make all your efforts worth the trouble.
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Dig out the jagged top of the pomegranate, using your fingernails or another sharp utensil such as the end of an old-fashioned bottle opener or the tip of a fingernail file. Leave the white, pithy top of the fruit intact.
Score the pomegranate into quarters by making very shallow cuts down the sides of the fruit's thin skin. Avoid cutting into the fruit itself -- you only want a deep enough cut to allow the skin to peel back.
Place your thumbs around the edges of the white, pithy top of the pomegranate. Press down firmly and pull the pomegranate apart. Pull off a portion of the skin if the pomegranate doesn't break in half.
Press down and pull apart the fruit again until you have sections with the seeds showing. You may end up with four or five large pieces instead of four equal quarters.
Bend each section back to make it easier to remove the seeds with your fingers. Remove any white pith or membrane remaining on the seeds.