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For an extended three‐dimensional network (made up of a single type of structural unit) with an average C structural units sharing a vertex, the degrees of freedom, f, per vertex are

(5)

If f is positive, a network can exist. When f is negative, a TD network cannot exist. Thus, f = 0 provides a boundary for the existence of TD networks.

If additional constraints (θ) are present at the shared corners (for example, bond angle constraints) or if there are internal degrees of freedom (h) within the structural units (for example, there is one internal degree of freedom in a unit made up of a pair of edge shared tetrahedra), then Eq. (5) can be modified as follows:

(6)

The degrees of freedom of TD networks are also listed in Table 1 for several rigid structural units for different values of connectivity. It should be noted that SiO₂ with V = 4, C = 2, δ = d = 3 satisfies the condition of isostaticity (f = 0). Similarly, a two‐dimensional TD network of corner‐sharing rigid triangles (a candidate structure of B₂O₃ glass) is also isostatic.