What question did this study set out to answer?

The aim is to establish a periodic table structure based on the geometry of a truncated octahedron.

March 25, 2026Open Access

The Periodic Table Structure from Planck-Scale Foam Geometry

Q: What does this research mean for the field?

The complete structure of the periodic table, including subshell capacities, period lengths, and Madelung ordering, can be mathematically derived from the O_h crystal field splitting of the truncated octahedron representing Planck-scale foam geometry, with zero free parameters. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

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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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Luke Martin

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The Periodic Table Structure from Planck-Scale Foam Geometry

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