We construct self-consistent spherically symmetric solitonic configurations arising from a five-dimensional scalar field compactified on the orbifold S1/Z6. We derive the full Einstein–Klein–Gordon (EKG) system from the 5D action, perform the dimensional reduction explicitly, reduce the coupled equations to a first-order autonomous system, and solve them by eigenvalue shooting with the asymptotic normalization A(rmax) = 1. Sector n = 1 lies in the weak-field regime (lapse departure ∼22%), while n = 2 exhibits significant gravitational backreaction (Bmax ∼ 1.9, eigenvalue shift ∼48%), demonstrating that self-consistent treatment is essential beyond the lowest sector. We derive the asymptotic power-law tail exponents rigorously via indicial analysis for general compactification growth rate β, establish a Noether charge closure identity locking the compact-direction energy, and assess orbital stability by branch-following of the Q(ω∗) curve. The solution family exhibits a turning point characteristic of self-interacting boson stars; we estimate the instability timescale and argue it exceeds the cluster dynamical time for the configurations of interest. Self-consistent tidal truncation in the Perseus cluster environment yields sector-dependent radii (rt ≈ 6.2 kpc for n = 1, 9.0 kpc for n = 2) and enclosed masses in the range 4 × 109–1010 M⊙, lifting the degeneracy present in fixed-background treatments. We compute projected density profiles Σ(R) suitable for confrontation with imaging constraints on CDG-2, and show that the oscillatory radial structure distinguishes these configurations from fuzzy dark matter solitons. A self-contained proof that Z6 is the minimal admissible orbifold group is provided. Keywords: extra dimensions, Kaluza–Klein, boson stars, Q-balls, solitonic dark matter, fuzzy dark matter, dark galaxies, Perseus cluster
Noël Copinet (Thu,) studied this question.