Discovering novel families of molecular polyhedra through graph theory has attracted increasing interest. Nevertheless, the design principles of molecular polyhedra based on graph theory remain elusive, especially for those containing five-node units. Herein, we construct a series of chiral truncated face-rotating polyhedra (T-FRP) from pentagonal pentaphenylpyrrole (PPP) derivatives and chiral diamines. Graph theory is used to elucidate the geometry of these novel T-FRP, which represent a new family of molecular polyhedra. The phenyl flipping of PPP faces in these T-FRP is significantly restricted, thus making T-FRP chiral and strongly emissive in solution. In addition, T-FRP also generate circularly polarized luminescence. This study provides new insights into the rational design of novel molecular polyhedra through graph theory.