The basic systems of connected points

However complex the units that are to be joined together the problem may be reduced to the derivation of systems of points each of which is connected to some number (p) of others. In the simplest systems this number (the connectedness) is the same for all points  

It is not necessary to include singly-connected points (p = 1) in nets since they can play no part in extending the net. Also 2-connected points may be added along the links of any more highly connected net (p 2) without altering the basic system of connected points. We therefore do not include either 1- or 2-connected points when deriving the basic nets though it may be necessary to add them to obtain the structures of actual compounds from the basic nets. For example, 

2- connected points (representing -0- atoms) are added along tl edges of the 

3- connected tetrahedral group of four P atoms to form the P4O6 molecule, and additional singly-connected points (representing =0 atoms) at the vertices to form P4O1 0- 

In chain structures the repeating unit may be a single atom or a group of atoms  

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The basic systems of connected points, polyhedra, plane, and 3D nets are summarized in Table 3.7, which shows that the four plane and four 3D nets form series with n = 6, 5, 4, and 3, and with n = 10, 8, 6, and 4 respectively. All systems on the same horizontal line are composed of n-gon circuits, and all those in a... 

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