Pentagon-based topology

A. Muller, P. Kogerler, A. W. M. Dress, Giant Metal-Oxide-Based Spheres and Their Topology from Pentagonal Building Blocks to Keplerates and Unusual Spin Systems. Coord. Chem. Rev. 2001, 222, 193-218. 

Fig. 64e shows a [1102(804)2] chain that can be considered as based upon the cl/lb chain topology with each black vertex having a double link to the additional white vertex. Replacement of the latter by a grey vertex results in a chain shown in Fig. 64f Here grey vertices correspond to the NOs triangular groups that share edges with the UO7 pentagonal bipyramids.

A particularly novel 2D net based on pentagons (which cannot tessellate in two dimensions) is also known. The net topology is (5, ) in Wells nomenclatnre, meaning that it is composed of 3- and... 

Previous theoretical investigations of pure boron clusters, based on ab initio quantum chemical and density functional theoretical methods, have shown that pure boron has stable structures forming a new class of boron materials. These structures can be classified into four topological groups convex, spherical, quasiplanar and tubular clusters. The new forms contain basically two units a pentagonal and an hexagonal pyramid. All these clusters can easily be generated by both units with the help of an Aufbau Principle proposed for boron. ... 

Buckminsterfullerene. an allotrope of carbon, is topologically equivalent to a truneated ieosahedron, an Archimedean solid based on 12 pentagons and 20 hexagons (Fig. 5c).Eaeh earbon atom of the framework corresponds to a vertex of the polyhedron. As a result, C o is held together by 90 eovalent bonds, the number of edges of the solid. 

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