Enumeration of four-connected three-dimensional nets. I. Conversion of all edges of simple three-connected two-dimensional nets into crankshaft chains

Abstract

Various topological approaches to mathematical analysis, classification and enumeration of four-connected three-dimensional (3D) nets are listed. Four-connected 3D nets are being generated systematically by conversion of edges of a vertical stack of congruent three-connected two-dimensional (2D) nets into chains. This paper describes 57 3D nets obtained by converting into crankshaft chains all edges of the simpler 2D nets in the catalog of the Consortium of Theoretical Frameworks. Atomic coordinates are given for distance-least-squares modeling in the highest space group. Nine nets occur in known structures: tridymite, Zn2P2O8 \cdot organic, aluminophosphates AlPO-5 (International Zeolite Association Structure Commission code AFI), AlPO-8 (AEI), AlPO-11 (AEL), AlPO-25 (ATV), AlPO-41 (AFO), AlPO-54 (VFI) and AlPO-H2 (AHT).