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Take a medium or large carrot, and use a vegetable peeler to remove the skin. After peeling the carrot, use a sharp knife to cut it in half, thirds, or quarters, depending on the size of the carrot. The pieces should be approximately 3-inches (8-cm) long. You don't necessarily have to peel the carrots. If you're using organic carrots, the skin is usually thin enough to eat. Take each section of carrot, and use a knife that you feel comfortable making precise slices with to cut long, shallow wedges along the entire length the carrot piece to form the flowers' petals. You'll want to make 5 to 6 wedges around each piece of carrot. It helps to hold the carrot piece upright when you're cutting out the wedges. Balance it against a cutting board with one hand, and use the other to cut. Once you've cut out wedges around the entire piece of carrot, place it horizontally on the cutting board, and use your knife to slice it into coins that are approximately -inch (-cm) thick. Each coin will be a small flower.
Peel the carrots and cut into pieces. Cut grooves into the carrot pieces with a knife. Slice the lengths of carrot into coins.