A closed surface in three-dimensional space, using the triangular meshes to discrete, with half edge structure will be stored in the computer. This work will have three different types of closed surface (ball, genus of one, genus of two) to discuss, For the closed surface to cut, cutting down the cut graph able to transform surfaces into different types of fundamental domain, and thus created covering space. Working cut graph on closed surface of the three-dimensional using two different algorithms with different weights to control generated cut graph. Different algorithms with different weights, get different cut graph, but cut graph does not completely in accordance with the original design weight hope.