This mathematical exploration proves geodesic triangulation minimizes conformal variance, highlighting its unique properties.
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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Yoshimitsu Katayama (2026) studied this question.
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