Researchers strive to produce nanoparticles with complexity in composition and structure. Although traditional spherical, cylindrical and membranous, or planar, nanostructures are ubiquitous, scientists seek more complicated geometries for potential functionality. Here we report the simple solution construction of multigeometry nanoparticles, disk-sphere and diskcylinder, through a straightforward, molecular-level, blending strategy with binary mixtures of block copolymers. The multigeometry nanoparticles contain disk geometry in the core with either spherical patches along the disk periphery in the case of disk-sphere particles or cylindrical edges and handles in the case of the disk-cylinder particles. The portions of different geometry in the same nanoparticles contain different core block chemistry, thus also defining multicompartments in the nanoparticles. Although the block copolymers chosen for the blends are important for the definition of the final hybrid particles, the control of the kinetic pathway of assembly is critical for successful multigeometry particle construction.