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This is a mathematical question raised from engineering and physics:

Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For example, a triangular lattice can be filled with basis to getfilling

While enter image description here alone cannot give any filled colored graph. Is there any general systematic mathematical approach in solving this problem?

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Is it allowed to rotate a basis element in using it to build the pattern? –  coffeemath Nov 8 '13 at 21:42
    
Yes. You can perform symmtey operations on the basis. –  user40780 Nov 8 '13 at 21:55
    
Cross-posted at mathoverflow.net/q/147374/12357 –  Joel Reyes Noche Nov 9 '13 at 0:37
    
@user40780, please do not simultaneously cross-post the same question across different StackExchange sites. This is frowned upon because it leads to duplication of effort. –  Joel Reyes Noche Nov 9 '13 at 0:38
    
Also cross-posted at physics.stackexchange.com/q/83855 –  Joel Reyes Noche Nov 9 '13 at 8:55
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