A photonic band gap (PBG) is a range of frequencies in which no propagating states of light
exist. PBGs can be engineered using dielectric arrangements structured on the length scale of
the light’s wavelength. Many biological species, from plants to insects, use this mechanism to
produce structural color through periodically crystalline and amorphous networks. These nets
can be characterized by their coordination number statistics - the number of edges joined at
each vertex. Crystalline nets are well understood but show an intrinsically anisotropic optical
response. Among these, the diamond net with a coordination number of 4 exhibits the largest
known PBG. There are examples of disordered networks in nature that exhibit a PBG
comparable to crystalline structures. An established Metropolis Monte Carlo algorithm
gradually transforms the diamond net into a disordered photonic structure. However, nature
employs other network geometries, such as the chiral gyroid, which has a coordination number
of 3. Here, we alter the conventional bond-bending energy in the Monte Carlo algorithm to
enable a generalization to arbitrary coordination numbers. The photonic response of three
networks with a mixed coordination number of 3 and 4 is investigated, and the band structure
of the crystalline and disordered networks is analyzed. The differences in the photonic density
of states of the network and a corresponding homogeneous medium are shown for these three
networks.