The platonic solid built with only squares is the Cube (Hexahedron). If you put a vertex on every face and connect them, you get its dual, an Octahedron. If you imagine the structure as of its faces and unfold it, you get its net. 

As part of the Platonic Solids series, this model has clearly defined colors outlining the solid itself, scaffolding in black, and its dual in white.