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March 31, 20260 citationsOpen Access

The Visible Spectrum from the Face Laplacian of the Truncated Octahedron

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LMLuke Martin

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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Cite This Study

Luke Martin (2026) studied this question.

synapsesocial.com/papers/69cb6589e6a8c024954b98e4https://doi.org/10.5281/zenodo.19306315
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Also Consider

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  1. 1The Visible Spectrum from the Face Laplacian of the Truncated Octahedron2026
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  4. 4The Pure Mathematics of the Kelvin Cell: Combinatorial Spectra, O_h Representation Theory, and the Quadratic Ring Q(√17)2026 · 4 citations
  5. 5The Dark Energy 6/7 Factor from Face Laplacian Topology2026