This paper presents a new design of aerial vehicles with tetrahedral geometry. We call this design the TetraQuad. The TetraQuad is a fractal modular aerial robot. A characteristic of fractals is that they have a geometric shape that can be assembled to generate the same geometry on a larger scale. Therefore multiple TetraQuad modules can be assembled to produce a larger scaled tetrahedral shaped aerial vehicle. The advantage is to have modular aerial robots that assemble in the vertical direction; this increases the rigidity of the structure, as well as reduces the wake interaction of the elevated propellers in the assembly. This work presents a design and analysis of the TetraQuad module as well as assemblies of multiple modules. A modular controller strategy is discussed. The functionality of the controller is illustrated using simulations. We validate our design with experimental flight tests.