The Make Group of Euler Operators:

The Make group contain four operators for adding up some elements into the existing model making a new one, and a Make-Kill operator for adding and deleting some elements at the mean time. Here are the operators :

The above table illustrated the change of values of V, E, F, L, S and G. Note down that adding a face produces a loop, the outer loop of that face. Thus, when F is increased, L must also be increased. This new loop and the new face shall cancel each other in the subexpression L - F. Please check that none of these operators would cause the Euler-Poincaré formula to fail.

Table illustrates the way of utilizing Euler operators to construct a tetrahedron. Vertices, edges, & faces are in red, blue and green; the merely shell is in transparent gray. The primary step utilizes MSFV to obtain a shell with a face and a vertex. The after that three steps use MEVs, each of which adds an edge & a vertex. The last three steps utilize MFE, each of which adds a face and an edge. Therefore, in seven steps or seven Euler operators a tetrahedron is constructed.