[x1, x2, x3, x4, x5]
x2+x3+x4+x5;
x1+x3+x4+x5;
x1+x2+x4+x5;
x1+x2+x3+x5;
x1+x2+x3+x4;
[[-0.5,1], [-0.5,1], [-0.5,1], [-0.5,1], [-0.5,1]]
# The linear function f_i(x)=\sum_{j\neq i} x_j in dimension 5. The degree of a linear function is just the sign of the determinant (assuming the box contains 0).