Wrap the next largest slice around it. Then wrap another slice in the opposite direction. Keep wrapping slices in opposite directions until the rose is complete. Use the largest slices for the outside petals, and insert two or three toothpicks into the base to secure them. Potatoes need more care because their slices even when paper-thin aren't as flexible as cucumber slices.
Some people use a carrot stick in the center to wrap the first potato slice around.
Stan Horstmanshoff, kitchen manager at the Delta Center, suggests a baby carrot for the center. Use the same method for potato roses as for cucumber ones, except don't use the water soak before making the rose. For a special edible garnish, soak the potato rose in cold water for five minutes, then deep-fry it. The frying will hold the petals together. He serves his dishes with long strands of shredded cheese or edible flowers, like peppery nasturtiums.