Automatically generated periodic graphs

作者：McColm Gregory^*

来源：Zeitschrift fur Kristallographie-Crystalline Materials, 2015, 230(12): 699-707.

DOI：10.1515/zkri-2015-1866

• crystal design
• geometric group theory
• periodic graph
• reticular chemistry
• turtle geometry

A crystal structure may be described by a periodic graph, so the automatic generation of periodic graphs satisfying given criteria should prove useful in understanding crystal structure and developing a theory for crystal design. We present an algorithm for constructing periodic graphs, based on a discrete variant of "turtle geometry," which we formalize using isometries represented as affine transformations. This algorithm is given information about the putative orbits (kinds) of vertices and edges and produces a finite graph which is then collapsed into a unit cell of a periodic graph. We verify that this algorithm will generate any periodic graph.

• 出版日期2015-12