A strongly aperiodic polycube

Dataset describing the construction of a strongly aperiodic polycube monotile derived from Tsiokos' Chair44 structure by carving Flicker's three-colour arrow rule into the 4×4 faces as unit-cube notches and bumps, one cell in from every face edge. The resulting tile comprises 448 unit cubes and forms a closed topological 3-ball. The dataset includes the tile’s cube coordinates, computational enumeration and verification code, and results for registered contacts, surrounding shells and notch-filler configurations. These support the proof that the tile admits tilings of three-dimensional Euclidean space by congruent copies, with reflections allowed, while its geometry forces lattice registration and a unique hierarchy of supertiles. Every tiling has no symmetry of infinite order; no colours, markings or additional matching rules are required.[updated 25-9-26: Version 1.1 adds smooth chair structures obeying Flicker's arrow rules that can be assembled, and extends both theorems from one tile to a family of six and replaces the pocket argument of version 1 by a shorter one; the argument of version 1 is kept in Appendix A.][updated 27-9-26: Version 1.2 corrects the remark on physical assembly in the note and adds the analysis behind it: a kinematic checker with exact convex features and a design-independent contact-graph analysis, which show that rigid tiles with any pull-out or sliding features can be assembled into the 8-tile supertile only with shallow pyramids and never into the 64-tile supertile. It adds a compliant snap-fit tile (rigid body with hollow TPU domes) whose layout leaves no undetectable wrong contact between same-handed copies, print-in-place patches of 8 and 64 tiles, and two interactive pages, one playing the tile-by-tile assembly and one explaining the hierarchy argument visually. All references now use the concept DOI.]