Understanding the liquid structure provides information that is crucial to uncovering the nature of the glass-liquid transition. We apply an aerodynamic levitation technique and high-energy X-rays to liquid (l)-Er(2)O(3)to discover its structure. The sample densities are measured by electrostatic levitation at the International Space Station. Liquid Er(2)O(3)displays a very sharp diffraction peak (principal peak). Applying a combined reverse Monte Carlo - molecular dynamics approach, the simulations produce an Er-O coordination number of 6.1, which is comparable to that of another nonglass-forming liquid,l-ZrO2. The atomic structure ofl-Er(2)O(3)comprises distorted OEr4 tetraclusters in nearly linear arrangements, as manifested by a prominent peak observed at similar to 180 degrees in the Er-O-Er bond angle distribution. This structural feature gives rise to long periodicity corresponding to the sharp principal peak in the X-ray diffraction data. A persistent homology analysis suggests thatl-Er(2)O(3)is homologically similar to the crystalline phase. Moreover, electronic structure calculations show thatl-Er(2)O(3)has a modest band gap of 0.6 eV that is significantly reduced from the crystalline phase due to the tetracluster distortions. The estimated viscosity is very low above the melting point forl-ZrO2, and the material can be described as an extremely fragile liquid.