The Visible Spectrum from the Face Laplacian of the Truncated Octahedron

Key Points

• The aim is to explore the relationship between the face Laplacian of a truncated octahedron and its spectral properties.
• Analysis of the face Laplacian on a 14-face truncated octahedron
• Examination of irreducible representations of O_h
• Calculation of wavelength ratio from derived spectral data
• Identification of 7 spectral bands corresponding to irreducible representations
• Derivation of the base wavelength ratio λ_max²/χ = C_A⁴/2 = 40.5
• Integration within the framework of Unified Foam Field Theory