With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n) = 1/6(n^3 + 3n^2 + 8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, ... (OEIS A003600).

cake cutting | circle division by lines | cylinder cutting | plane division by lines | square division by lines