The Geodesic Universe: Fuller's Spherical Geometry as the Physical Implementation of the Koku-Face Riemann Topology (v2)

Revised v2: Added Section 2.1b establishing the mathematical privilege of geodesic triangulation over arbitrary spherical triangulations. Proves that icosahedral geodesic subdivision uniquely minimizes conformal variance (σ²_conformal) among all discrete spherical approximations of equal face count, via the icosahedron's unique vertex/edge/face-transitivity (symmetry group order 120). Includes formal theorem statement and comparison table.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-18
DOI
https://doi.org/10.5281/zenodo.20740282
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

The Geodesic Universe: Fuller's Spherical Geometry as the Physical Implementation of the Koku-Face Riemann Topology (v2)

Yoshimitsu Katayama
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

The Geodesic Universe: Fuller's Spherical Geometry as the Physical Implementation of the Koku-Face Riemann Topology (v2)

Yoshimitsu Katayama
preprint en

Abstract

Revised v2: Added Section 2.1b establishing the mathematical privilege of geodesic triangulation over arbitrary spherical triangulations. Proves that icosahedral geodesic subdivision uniquely minimizes conformal variance (σ²_conformal) among all discrete spherical approximations of equal face count, via the icosahedron's unique vertex/edge/face-transitivity (symmetry group order 120). Includes formal theorem statement and comparison table.

Zenodo (CERN European Organization for Nuclear Research)
Bukhara State University (UZ)
Mathematics and Applications
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