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2 results for “rep-tiles”

Three-dimensional Rep-tilesmath.GT

This paper classifies all 3D rep-tiles up to homeomorphism.

problem Identifying compact 3D shapes that can be tiled into smaller copies of themselves.

method Examined all 3D rep-tiles up to homeomorphism, showing equivalence to the exterior of a connected graph in

S^3

result A 3-manifold is a 3D rep-tile if and only if it is the exterior of a connected graph in

S^3

3D rep-tiles compact 3-manifolds homeomorphism rep-tiles graph exterior

2021-07-21abs ↗pdf ↗

Rep-Tilesmath.GT

Rep-tiles fill cubes in any dimension.

problem Finding compact submanifolds that can tile cubes.

method Classifying and constructing rep-tiles for any finite CW complex.

result Every smooth compact submanifold with connected boundary is topologically isotopic to a rep-tile.

rep-tiles submanifolds tiling polycubes homotopy

2024-12-28abs ↗pdf ↗