GATE 2020 PH – Question 29
For the two-dimensional lattice shown, find the number of distinct primitive-cell constructions intended by the figure.
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Correct answer: 5 to 5
Explanation
A primitive cell has area equal to the area per lattice point and contains one point after boundary sharing. For the centred square pattern shown, the standard constructions using the illustrated nearby lattice points give the central diamond and four neighbouring slanted parallelograms, totaling five. Thus the keyed count is 5. Without the restriction implicit in this diagram-based convention, arbitrary unimodular changes of primitive vectors generate infinitely many valid primitive cells.