We establish a correspondence between the dimer model on bipartite graph and circle pattern with combinatorics of that graph, which holds for graphs are either planar or embedded torus. The set positive face weights gives global coordinates space patterns dual. Under this correspondence, extends previously known isoradial case, urban renewal (local move models) is equivalent to Miquel patterns)...

Polycyclic Hydrocarbons. In their Communication (e202304937), Chunyan Chi et al. report the synthesis and isolation in single-crystal form of two fused indacene dimer isomers. Both isomers display an open-shell singlet ground state.

In the title compound, 2C(6)H(7)N(2)O(2) (+)·SO(4) (2-)·3H(2)O, there are two independent cations which are connected into N-H⋯O hydrogen-bonded dimers. In the crystal, O-H⋯O hydrogen-bonded sulfate-water sheets run parallel to (001) and are linked into a three-dimensional network via inter-molecular N-H⋯O and O-H⋯O hydrogen bonds through the 2-amino-nicotinium dimers. Further stabilization is ...

A general method for synthesizing a novel class of metalloporphyrin dimers containing unbridged metal-metal bonds is presented. By choosing the appropriate metal, the bond order in these dimers can be varied systematically. The synthesis and characterization of osmium(II) and molybdenum(II) porphyrin dimers containing the respective metal-metal double and quadruple bonds are described. A simple...