We show, using density functional theory and ab initio molecular dynamics, that certain small colloidal quantum dots with a mixed nanocrystal core capped with achiral surface ligands spontaneously form a triskelion (from the Greek, three-legged) structure with (approximate) C3 symmetry that can be dynamically stable at room temperature when additionally capped with small amine ligands. Furthermore, the nanocrystal core also forms a triskelion structure. The focus of our study is a colloidal quantum dot with a Cd16Se7Te3 core (and a charge of +12) capped with negatively charged surface ligands to achieve charge neutrality-in the simplest instance, 12 Cl--to form the colloidal quantum dot Cd16Se7Te3Cl12. The small size of the core (for which almost all atoms are surface atoms), the high positive charge that destabilizes the core, the mixed (Cd/Te) composition that creates mechanical strain in the core, and the inclusion of precisely three Te atoms in the predominantly Se core all play critical roles in the spontaneous formation of the triskelion structure.