v2009.01.01 - Convex Optimization

5.3. ∃ FIFTH EUCLIDEAN METRIC PROPERTY 351
k
θ ikl
θikj
θ jkl
i
l
j
Figure 94: Fifth Euclidean metric property nomenclature. Each angle θ is
made by a vector pair at vertex k while i,j,k,l index four points at the
vertices of a generally irregular tetrahedron. The fifth property is necessary
for realization of four or more points; a reckoning by three angles in any
dimension. Together with the first four Euclidean metric properties, this
fifth property is necessary and sufficient for realization of four points.