In Pickering-Ramsden emulsions, the packing structure of the colloidal particles at the liquid-liquid (or liquid-gas) interface significantly affects the structure and behavior of the emulsion. Here, using a series of platelike particles with regular polygonal shapes and Janus amphiphilicity, we created emulsion droplets stabilized by close-packed polygonal particles at the interface. The systematic variation of the particle morphology shows that the geometrical features of the regular polygons in (curved) planar packing dominate over the self-assembled structures. The structures are tessellations of triangular, square, and hexagonal particles at the surface for large droplets and regular tetrahedral, cubic, and dodecahedral particle shells of triangular, square, and pentagonal particles for small droplets, respectively. This work creates the possibility of geometrically designing the structure and functionality of emulsions.