For most block types in square, honeycomb, and cubic combinatorial metamaterials, arbitrary defect patterns are realizable, while some block types exclude many patterns; in 3D all defect lines form closed curves and can realize any knot or link.
4a shows a configuration of seven vertices that cannot be defected with this block type, provided that all other vertices are non-defected
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Defect Positioning in Combinatorial Metamaterials
For most block types in square, honeycomb, and cubic combinatorial metamaterials, arbitrary defect patterns are realizable, while some block types exclude many patterns; in 3D all defect lines form closed curves and can realize any knot or link.