Paper Cg develops the geometric architecture underlying Light Frame Cadence Theory (LFCT). The paper presents the Cadence Star as a two-form structural object with both a planar realization and a three-dimensional realization: the complete graph K6 on six signed mode-orientation vertices and the stella octangula (compound of two interpenetrating regular tetrahedra) with its inner octahedral carrier. The work establishes the explicit correspondence between the six-element signed mode set X = {TD, TS, TR} × {±}, the K6 cadence face with binary resolution depth beta_1 = 10, and the stella octangula realization whose six inner octahedral vertices carry the signed modes while the eight outer cube vertices provide the ambient shell. The paper further identifies the operative LFCT symmetry subgroup G0 = C3 × Z2 within the full octahedral symmetry group Oh and develops the equivariant projection connecting the three-dimensional and planar realizations. Two foundation-level theorems are stated and proved. The Cadence-Fixed Equivariance Theorem establishes that the operative subgroup acts as a graph automorphism of K6 while preserving the cycle-space decomposition. The Cadence Star Rotation Phase Update Law formalizes the discrete C3 phase action that underlies LFCT's rotation architecture and loader-rotation cycle. Paper Cg serves as the geometric companion to the LFCT Foundation Axioms. It provides the explicit mathematical realization of the Cadence Star architecture, consolidating the framework's planar K6 reading, stella octangula realization, operative symmetry structure, equivariant projection, and F1/F2/F3 fabric-depth instantiations into a single geometric foundation reference.