Platonic Solids are the most regular polyhedra: all faces the the same regular polygon, and they look the same at every vertex. The Greek philosopher Plato discovered that there are only five solids with these properties. He belied that the they correspond to the four ancient Elements, Earth, Water, Air and Fire, as well as the Universe.
Archimedean Solids, like the Platonic ones, consist of regular Polygons and look the same at every vertex. However the faces are multiple different regular polygons. There are 13 Archimedean Solids, two of which are reflections of each other.