English: A fundamental domain in logarithmic space of the group of units of the number field K obtained by adjoining to Q a root of f(x) = x³ + x² − 2x − 1. This field is a Galois extension of degree 3. Its discriminant is 49 = 7². If α denotes the root of f(x) which is approximately 1.24698, then a set of fundamental units is {ε₁, ε₂} where ε₁ = α² + α − 1 and ε₂ = 2 − α². The fundamental domain is spanned by v₁ and v₂ with the ith component of v_j equal to log|σ_i(ε_j)|. So, approximately, v₁ = (0.588863, −0.809587, 0.220724) and v₁ = (−0.809587, 0.220724, 0.588863). The area of the fundamental domain is approximately 0.910114, so the regulator of K is approximately 0.525455. See Table B.4 of Cohen's A course in computational algebraic number theory (1993). Computed using PARI/GP. Plotted using Mathematica.