The Icosidodecahedron Pair: Register Reconstruction, Full Archive Version to Follow (INDYNA Research Note 16)

Abstract

The icosidodecahedron (30 vertices, shells $\cos\theta\in\{\pm\varphi/2,\pm1/2,\pm1/(2\varphi),0\}$) is the mirror-class prototype of INDYNA: its two-shell operator $M(g)=A_1+gA_2$ has the exact crossing-free ground line $E_0=-2(1+g)$, the rational family that later defines the mirror class of the two-class law (Register L148) and the corrected Keplerat prediction for $\{$Mo$_{72}$Fe$_{30}\}$. Its conjugate shell pair $\pm\varphi/2\leftrightarrow\mp1/(2\varphi)$ realises the band–shadow-band mechanism on the smallest Archimedean carrier. The paired analysis ("Paar 2") of the companion body resides in the author's archive and will be supplied as the full version of this note; the present reconstruction fixes the numbering and the theorem content from the law register (L78, L148). Licence CC-BY-4.0. Continues: Note 15. Supplement to: INDYNA Law Register. Part of the INDYNA Notes series (Notes 16–34). All numbers reproduce from the INDYNA law register (master data record, doi:10.5281/zenodo.21891088). Licence CC-BY-4.0.