  This paper addresses formation control of reduced attitudes in which a
continuous control protocol is proposed for achieving and stabilizing all
regular polyhedra (also known as Platonic solids) under a unified framework.
The protocol contains only relative reduced attitude measurements and does not
depend on any particular parametrization as is usually used in the literature.
A key feature of the control proposed is that it is intrinsic in the sense that
it does not need to incorporate any information of the desired formation.
Instead, the achieved formation pattern is totally attributed to the geometric
properties of the space and the designed inter-agent connection topology. Using
a novel coordinates transformation, asymptotic stability of the desired
formations is proven by studying stability of a constrained nonlinear system.
In addition, a methodology to investigate stability of such constrained systems
is also presented.
