Finite polyhedral fits: discrete scale jumps, orientational domains, and contact structure in 351 certified constructions

Packing a finite number of congruent polyhedra inside a polyhedral container produces pronounced changes in required container size as the number of pieces increases. Some adjacent counts share a construction scale, while other additions require a substantial expansion. We study 351 certified constructions in nine ordered pairs of Platonic solids, with every count from 2 through 40. Five pairs use the same solid for pieces and container; four use mixed pairs. We distinguish the exact feasible scale of each archived construction, the numerically estimated touching limit, and a monotone feasible envelope obtained by deleting pieces from larger constructions. We analyze absolute and relative scale increments, occupied volume fraction, orientational similarity modulo the proper rotational symmetry group of the piece, and graphs of near contacts determined by Euclidean feature distances. Contact-connected orientational domains provide a precisely defined geometric proxy for grains, while avoiding a claim of physical crystallization. The archive exhibits long count plateaus, sharp expansion steps, aligned and dispersed orientations, and large differences between raw edge scale and volume-normalized efficiency. None of these observations establishes global optimality. Closed-form labels attached to numerical touching limits remain conjectures unless supported by an independent symbolic construction. The accompanying machine-readable tables, source hashes, scripts, and figures expose every calculation and provide a basis for experiments on confinement, orientational organization, and lower-bound proofs. Tools used: Claude (Anthropic) assisted computational development under the author's direction; Codex assisted source inspection, reproducibility checks, quantitative analysis, and manuscript drafting and exposition. Computational tools are described in the methodology. Alejandro Zarzuelo Urdiales is the human author responsible for the work; no AI system is listed as an author. Scientific source snapshot: e15b496ae7306287e0e70bb5b14be79f5dfdde84. The data cover 351 stored configurations in nine shape pairs and every count from 2 to 40. Exact feasibility certificates establish stored upper bounds, not general global optimality. The source repository provides inspectable construction files and certificates.