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March 25, 20260 citationsOpen Access

The Periodic Table Structure from Planck-Scale Foam Geometry

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LMLuke Martin

Key Points

  • The aim is to establish a periodic table structure based on the geometry of a truncated octahedron.
  • Analyzed O_h crystal field splitting of a truncated octahedron
  • Identified four subshell types through irrep decomposition
  • Calculated subshell capacities using irrep dimensions and spin degeneracy
  • Ordered subshells based on face Laplacian eigenvalues
  • Derived maximum angular momentum from geometry
  • Confirmed subshell capacities of 2, 6, 10, and 14
  • Established period lengths of 2, 8, 8, 18, 18, 32, 32
  • Determined maximum angular momentum l = 3 for 14-face cell geometry
  • Defined inter-shell ordering through a consistent derivation chain
  • Eliminated free parameters in the model

Abstract

The periodic table structure derived from Oₕ crystal field splitting of the truncated octahedron. Four subshell types (s, p, d, f) from irrep decomposition. Subshell capacities (2, 6, 10, 14) from irrep dimensions × spin degeneracy. Period lengths (2, 8, 8, 18, 18, 32, 32). Intra-shell ordering from face Laplacian eigenvalue ordering. Maximum angular momentum l = 3 from 14-face cell geometry. The Madelung inter-shell ordering derivation chain established. Zero free parameters.

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Cite This Study

Luke Martin (2026) studied this question.

synapsesocial.com/papers/69c37bf3b34aaaeb1a67ee7dhttps://doi.org/10.5281/zenodo.19185628
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