I03Available
Square Kolam Tile Challenge
Use all sixteen globally oriented tiles to build one connected nonzero kolam on a 4 × 4 board.
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Active now4 interactives
Kolam Tiles
Binary kolam tiles on square boards and polyhedral surfaces: local matching, global connectivity, graph structure, symmetry, puzzles, and interactive constructions.
Open project in the LabThe investigation
What global forms emerge when binary kolam tiles are assembled under local edge-matching rules?
The square branch encodes the sixteen four-bit words as globally oriented tiles. Adjacent bits must match, the boundary must close, and the fifteen nonzero tiles must form one connected network.
Removing the 0000 tile produces a labelled 15-puzzle, bringing parity and orbit structure into the problem of moving between valid boards.
The triangular branch places the eight three-bit words on an octahedron; the dual cube converts the classification into a forced seven-vertex tree with three arm-length patterns.
KolamsCombinatoricsGraph theorySymmetry
Try it yourself
Interactives in this project
I04Available
Slide to a New Kolam
Move tiles through the open cell while preserving a correct square kolam, and watch the orbit invariant.
I05Available
Move X to Y
Transform one completed kolam into another and compare two configurations in the same 15-puzzle orbit.
I06Available
Kolams on an Octahedron
Compare three connected triangular kolam nets, fold each into an octahedron, and explore the completed solid.
Method & scope
How this project works
The current public project connects square-tile puzzles and triangular-tile polyhedra through graphs, symmetry and interactive constructions.
Interactives last tested 29 July 2026.