Meeting Observers, the Two Golden Icosahedra of the Stella Octangula, and the Body-Diagonal Axis of the A7 Crystals (INDYNA Research Note 36)

Abstract

In the INDYNA register an observer is a locked cube, the union T∪−T of the two tetrahedra of the stella octangula (L272). We compute exactly what observers share when they meet, in three and in four dimensions; we locate the icosahedron inside the pair of tetrahedra — not in either half, but in their common octahedron, in exactly two mirror forms — and relate this position to the rare-earth icosahedra of the Tsai-type 1/1 approximants; and we identify the body diagonal of the stella octangula as the displacement axis of the A7 elements As, Sb and Bi, while showing that the size of the displacement is not a fixed geometric constant.