We have calculated the figure of equilibrium of a rapidly rotating, differentiated body to determine the shape, structure, and composition of the dwarf planet Haumea. Previous studies of Haumea's light curve have suggested Haumea is a uniform triaxial ellipsoid consistent with a Jacobi ellipsoid with axes ≈ 960 × 774 × 513 km, and bulk density ≈ 2600 kg m −3 . In contrast, observations of a recent stellar occultation by Haumea indicate its axes are ≈ 1161 × 852 × 523 km and its bulk density ≈ 1885 kg m −3 ; these results suggest that Haumea cannot be a fluid in hydrostatic equilibrium and must be partially supported by interparticle forces. We have written a code to reconcile these contradictory results and to determine if Haumea is in fact a fluid in hydrostatic equilibrium. The code calculates the equilibrium shape, density, and ice crust thickness of a differentiated Haumea after imposing (semi-) axes lengths a and b. We find Haumea is consistent with a differentiated triaxial ellipsoid fluid in hydrostatic equilibrium with axes of best fit a = 1050 km, b = 840 km, and c = 537 km. This solution for Haumea has ρ avg = 2018 kg m −3 , ρ core = 2680 kg m −3 , and core axes a c = 883 km, b c = 723 km, and c c = 470 km, which equates to an ice mantle comprising ∼ 17% of Haumea's volume and ranging from 67 to 167 km in thickness. The thick ice crust we infer allows for Haumea's collisional family to represent only a small fraction of Haumea's pre-collisional ice crust. For a wide range of parameters, the core density we calculate for Haumea suggests that today the core is composed of hydrated silicates and likely underwent serpentinization in the past.