A glance at the expression
is sufficient to verify the fact that it is symmetric with respect to a, b, c, d, and also with respect to α, β, γ, δ. It is likewise, although not quite so evidently, an alternating function with respect to the interchange
that is to say, if a and α be interchanged, and at the same time b and β, c and γ, d and δ, the function is not altered in magnitude, but merely changes sign. With a little trouble, indeed, the expression can be transformed into
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