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We compute the complete Fadell-Husseini index of the 8 element dihedral groupD_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. Thisestablishes the complete goup cohomology lower bounds for the two hyperplanecase of Gr"unbaum's 1960 mass partition problem: For which d and j can any jarbitrary measures be cut into four equal parts each by two suitably-chosenhyperplanes in R^d? In both cases, we find that the ideal bounds are notstronger than previously established bounds based on one of the maximal abeliansubgroups of D_8.

The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes