function [BOOL] = chk_Euler_rule(V, F)
    V_n = size(V, 1);
    F_n = size(F, 2);
    arr = zeros(V_n, V_n);

    for i = 1 : F_n
        a = F(1, i);
        b = F(2, i);
        c = F(3, i);

        if a < b
            arr(a,b) = 1;
        else
            arr(b,a) = 1;
        end

        if a < c
            arr(a,c) = 1;
        else
            arr(c,a) = 1;
        end

        if b < c
            arr(b,c) = 1;
        else
            arr(c,b) = 1;
        end
    end

    E_n = sum(arr(:) == 1);
    BOOL = (V_n - E_n + F_n) == 2;



function [] = show()
    [V, F] = off('sphere.off');
    trimesh(F, V(:,1), V(:,2), V(:,3));



function [V, F] = off (filename)
    fid = fopen(filename, 'r');
    str = fgets(fid);
    p = fscanf(fid,'%d %d %d\n', 3);
    V = fscanf(fid,'%f %f %f\n', [3 p(1)]);
    V = V';
    F = fscanf(fid,'%d %d %d %d\n', [4 p(2)]);
    F = F(2:4,:)+1;
    F = F;
    fclose(fid);