  Crystal structure design is important for the discovery of new highly
functional materials because crystal structure strongly influences material
properties. Crystal structures are composed of space-filling polyhedra, which
affect material properties such as ionic conductivity and dielectric constant.
However, most conventional methods of crystal structure prediction use random
structure generation methods that do not take space-filling polyhedra into
account, contributing to the inefficiency of materials development. In this
work, we propose a crystal structure generation method based on discrete
geometric analysis of polyhedra information. In our method, the shape and
connectivity of a space-filling polyhedron are represented as a dual periodic
graph, and the crystal structure is generated by the standard realization of
this graph. We demonstrate that this method can correctly generate
face-centered cubic, hexagonal close-packed, and body-centered cubic structures
from dual periodic graphs. This work is a first step toward generating
undiscovered crystal structures based on the target polyhedra, leading to major
advances in materials design in areas including electronics and energy storage.
