  I consider the momenta and conserved quantities for CP^2 interpreted as the
space of quadrilaterals. This builds on seminar I and II's kinematics via
making use of MacFarlane's work considering the SU(3)-like (and thus particle
physics-like) conserved quantities that occur for CP^2. I perform the
additional step of further interpreting that as the configuration space of all
relational quadrilaterals and thus an interesting toy model for whole-universe,
relational and geometrodynamical-analogue physics. I also provide the Kuchar
observables for the quadrilateral, which is a particular resolution of the
Problem of Observables. I study HO-like and highly symmetric potentials. I also
provide some exact solutions and qualitative behaviours for dynamics on CP^2.
In each case, I reinterpret the results in terms of quadrilaterals. This paves
the way for the quantum mechanical study of the relational quadrilateral and
for investigations of a number of Problem of Time strategies and of a number of
other foundational and qualitative investigations of Quantum Cosmology.
