A new simply connected three-dimensional monotile, called Chair44 (R44), is presented that forces aperiodic tilings by shape alone. R44 is a rational polyhedral 3-ball formed from a seven-cube chair whose 24 exposed unit panels carry tiny square-pyramid features that encode local contact rules. Allowed congruent copies (reflections permitted) tile all of R^3 but never with a translational period; every tiling is homochiral, admits a unique infinite hierarchy of nested supertiles, and has a symmetry group of order at most 24. The construction answers a question of Socolar and Taylor by avoiding screw motions or periodic stacking directions that afflict earlier examples such as the Schmitt-Conway-Danzer biprism and the 3D Socolar-Taylor design.
The correctness argument combines a geometric proof that the surface features force registration to a lattice with exhaustive finite enumeration and a single finite machine-checked test: the tile’s contact rule survives coarsening so decoded parent tilings must obey the same rule. A companion census was independently replayed by two implementations, and every finite gate and the written geometric lemmas and logical assembly are formalized as Lean 4 theorems (kernel-checked modulo specified compiler hooks), producing a tightly verified proof submission supported by computational certification.
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