Deltahedra fluxionality/rigidity

A polyhedron with e edges has e distinct dsd situations if at least one of these dsd situations is degenerate by satisfying Equation (1.10), then the polyhedron is inherently fluxional [40]. The inherent rigidity/fluxionality of the most important deltahedra including the most spherical deltahedra found in boranes (Figure 1.4) is summarized in Table 1.1. 

This simple analysis indicates that in deltahedral structures the 4, 6,10, and 12 vertex structures are inherently rigid the 5,8,9, and 11 vertex structures are inherently fluxional and the rigidity of the seven-vertex structure depends upon the energy difference between the two most symmetrical seven-vertex deltahedra [40]. From the point of view of coordination chemistry, note that the trigonal bipyramid and bisdisphenoid, which are favored coordination polyhedra for... 

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