Luminescent semiconducting quantum dots (QDs) are central to emerging technologies that range from tissue imaging to solid-state lighting. However, existing samples are heterogeneous, which has prevented atomic-resolution determination of their structures and obscured the relationship between their atomic and electronic structures. Here we report the synthesis, isolation, and structural characterization of three cadmium selenide QDs with uniform compositions (Cd35Se20(X)30(L)30, Cd56Se35(X)42(L)42, Cd84Se56(X)56(L)56; X = O2CPh, L = H2N-C4H9). Their UV-absorption spectra show a lowest energy electronic transition that decreases in energy (3.54 eV, 3.26 eV, 3.04 eV) and sharpens as the size of the QD increases (fwhm = 207 meV, 145 meV, 115 meV). The photoluminescence spectra of all three QDs are broad with large Stokes shifts characteristic of trap-luminescence. Using a combination of single-crystal X-ray diffraction and atomic pair distribution function analysis, we determine the structures of their inorganic cores, revealing a series of pyramidal nanostuctures with cadmium terminated {111} facets. Theoretical and experimental studies on these materials will open the door to a deeper fundamental understanding of structure-property relationships in quantum-confined semiconductors.