Table 5. Bond topology table for ^AGd^3+BMn³⁺O₃, showing numerical solution of its a priori bond valences (v.u.) and a priori bond lengths (in parentheses, in Å).

Bonds are variables a to d, and arrows represent bond multiplicity.

	A (Gd3+)	B (Mn3+)	∑
X1 (O2−)	a ×2↓ ×2→	c ×2↓ ×2→	2
	0.441 (2.343)	0.559 (1.966)
X2 (O2−)	b ×6↓×3	d ×4↓ ×2→	2
	0.353 (2.439)	0.471 (2.009)
∑	3	3