The Bodhi Seed: twelve rhombic triacontahedra and one more inside a triacontahedron φ² times larger, with the gap filled exactly

A rhombic triacontahedron RT(φ²) of edge φ² holds twelve RT(1) of edge 1, one on each five-fold axis and each pushed out until it touches the outer form, and one RT(1/φ) at its centre, without overlap. Each of the twelve touches five others face to face, in the pattern of the icosahedron's 30 edges. These are the counts and ratios of the Lotus seed (an icosahedron of edge φ² holding 12 icosahedra of edge 1 and one of edge 1/φ), and among the icosahedral solids tested on their 5-, 3- and 2-fold axes only the icosahedron and the rhombic triacontahedron close in this way. The gap, 31.8% of the volume (by volume 80 prolate and 20 oblate golden rhombohedra of edge 1, though these do not tile it), fills exactly with convex pieces in two ways, each of three types and each invariant under the full icosahedral group: kit A, 60 + 60 + 60 mirror-symmetric pieces; kit B, 60 Vajras (triangular bipyramids), 20 Crown Jewels (one in each outer three-fold corner, 14 corners) and 60 + 60 Diadems of opposite hands. Every corner is exact and every dihedral angle is a multiple of 6°. The twelve enclose exactly a rhombic hexecontahedron of edge 1 (20 prolate golden rhombohedra), so the inner pocket, the hexecontahedron minus the centre, has exactly the volume of RT(1). All pieces were checked pairwise free of overlap, with total volume exact. The layer of twelve triacontahedra around a rhombic hexecontahedron appears in S. Kabai's clusters; its closure inside RT(φ²), the centre, the exact kits and the growth as a seed were not found in the literature searched. Kit B (DICTO's names): 60 Vajra (triangular bipyramid, φ²O/6 = 0.205179), 20 Crown Jewel ((7φ − 3)O/2 = 1.957616), 60 Diadem L + 60 Diadem R (O/3 = 0.156743). Kit A: 60 Vajra, 60 B2 ((3 + 5φ)O/6 = 0.869152), 60 B3 (O/(3φ) = 0.096872). O = oblate golden rhombohedron of edge 1 (0.470228). The question, the golden-rhombohedron lead, the names and the hand-built twelve (Polyhedraverse) are DICTO's. Prior art: S. Kabai's clusters of rhombic triacontahedra around a rhombic hexecontahedron (Wolfram Demonstrations Project). Computation and checking were done with Claude (Anthropic). Files: the paper (PDF) and its data, scripts, logs and renders (zip; also at https://github.com/DICTOR-Master/kaleidohedra).