Imagine you are a turtle on an infinite sheet of paper and everywhere you go you draw a line. Consider the reciprocal of the primes from 3 to 1223, the decimal form of these numbers will always have a period. You, as a turtle, decide to guide your path according to these decimal digits, where a 0 means no turning and 9 means turning 9⁄10 of a full circle, these are the paths you draw.
2 and 5 are missing because they are boring.The resulting shapes are radially symmetrical and the number of slices is given by the difference in angle between the first rotation of each period, but in the naturals modulus 10. At the beginning of the first period the total rotation is zero, if at the beginning of the next period the total rotation increased by 2, then the shape will have 5 slices (2 * 5 ≡ 0 mod 10), if the difference is zero, then the shape will have 0 slices, making it a recurring pattern without radial symmetry (e.g. 61).