In this paper, I propose a holographic soft-wall model that incorporates a logarithmic correction to the linear mass spectrum of hadrons. The correction term is hypothesized to be proportional to (π − 3)/(4π), a number that naturally appears when discretizing a sphere by an icosahedron. Using experimental data on radial excitations of light, strange, charmed, and bottom mesons, I perform an analysis and find that the value β = 0.0106 ± 0.0022 obtained from a combined fit agrees well with (π − 3)/(4π) ≈ 0.01127. The model successfully describes known resonances and predicts masses for yet-unobserved states. A possible theoretical interpretation of β in terms of the anomalous dimension of the mass operator in QCD and its connection to the topology of the SU (3) gauge group is discussed.