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Which set of unit-cell parameters represents a cubic lattice, if the edge lengths are a, b, c and the interaxial angles are α, β, and γ?

1. a = b = c, with α = β = γ = 90°
2. a = b ≠ c, with α = β = γ = 90°
3. a = b = c, with α = γ = 90° and β ≠ 90°
4. a ≠ b ≠ c, with α = β = 90° and γ ≠ 90°

Correct answer: a = b = c, with α = β = γ = 90°

Solution

A cubic lattice has a = b = c with alpha = beta = gamma = 90. The stored a = b != c describes a tetragonal lattice, not cubic.

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