What question did this study set out to answer?

The aim is to explore the relationship between the face Laplacian of a truncated octahedron and its spectral properties.

March 31, 2026Open Access

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

Abstract

The 7 irreducible representations of Oₕ acting on the 14-face representation of the truncated octahedron map to 7 spectral bands. The base wavelength ratio λₘax²/χ = CA⁴/2 = 40. 5 is derived from the face Laplacian spectrum. Part XLVIII of the Unified Foam Field Theory.

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Luke Martin (Sun,) studied this question.

synapsesocial.com/papers/69cb6589e6a8c024954b98e4 https://doi.org/https://doi.org/10.5281/zenodo.19306315