The spontaneous emergence of periodic cellular structures from an isotropic fluid is a universal phenomenon in condensed matter physics. While the selection of the BodyCentered Cubic (BCC) phase via Brazovskii fluctuations has been well-established in systems where cubic invariants (Ψ3) are present, structural selection in systems possessing strict Z2 parity symmetry (Ψ → −Ψ) must arise purely from quartic 4-wave resonance interactions. In this paper, we present a systematic, self-contained analytical derivation demonstrating that the BCC structure remains the unique global minimum under strictly Z2-symmetric fluctuation mechanisms. By rigorously distinguishing between trivial antipodal planar combinations and non-trivial 3D skew quadrilaterals on the critical momentum shell, we exactly enumerate the 4-wave resonance loop multiplicity. We mathematically identify exactly 6 distinct non-trivial subsets for the BCC reciprocal star, compared to 2 for Face-Centered Cubic (FCC) and 0 for Simple Cubic (SC). Incorporating 1-loop Feynman vertex corrections, we analytically derive the explicit critical threshold where the massive phase-space volume forces a fluctuation-induced first-order transition strictly into the BCC state. By Fourier duality, this selected reciprocal state dynamically maps to a real-space Wigner-Seitz cell in the form of a 14-faced truncated octahedron, providing a rigorous geometric foundation for structural selection in Z2-symmetric pattern-forming systems.