Structures of solid crystalline materials (periodic crystals) are determined in a rigid form and hence keep all their properties under rigid motion within the same ambient environment. However, crystal structures that have different rigid shapes can substantially differ by properties and hence should be reliably distinguished, for example, polymorphs with different solubility. Conventional representations based on reduced cells discontinuously change under almost any perturbation of atoms, which led to the accumulation of near-duplicates in major databases of experimental structures [1]. This ambiguity was resolved by generically complete and continuous invariants that distinguish all non-duplicate periodic crystals in major databases within a few minutes on a modest desktop [2]. Now any dataset of experimental or simulated crystals can be visualized on maps with continuous and analytically defined invariant coordinates [3]. These invariants can be inverted to any generic periodic structure in 3 dimensions, uniquely under any distance-preserving transformation. Inspired by Richard Feynman's hint in Fig.1-7 of his first lecture on physics, the resulting Crystal Isometry Principle says that any real periodic material is uniquely determined by precise enough geometry of only atomic centers without chemical elements, under the same ambient conditions such as room temperature and normal pressure. [1] O.Anosova, V.Kurlin, M.Senechal. The importance of definitions in crystallography. IUCrJ 11 (4), 453-463 (2024). Many more near-duplicates are summarized at https://kurlin.org/projects/ultra-fast-duplicate-detection.pdf. [2] D.Widdowson, V.Kurlin. Resolving the data ambiguity for periodic crystals. Advances in Neural Information Processing Systems (NeurIPS), v.35, p.24625-24638 (2022). Extended version at https://arxiv.org/abs/2108.04798. [3] D.Widdowson, V.Kurlin. Continuous invariant-based maps of the Cambridge Structural Database. Crystal Growth & Design, 24(13), 5627–5636 (2024). More maps of the materials spaces are at http://arxiv.org/abs/2410.13796.