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Let V denote the set of vertices of P and let d _P denote the distance on V defined by dp( u, u ) = || u - u || ² dp\left( {u,υ} \right) = \left\| {u - υ} \right\|^2 for u, v H _{| V |: =} { d | å _{u, n e V} b _u b _n d( u, n ) \leqslant 0 {\mathcal{H}}_{\left| V \right|: = } \left\{ {\left. d \right|\sum\nolimits_{u,νεV} {b_u b_νd\left( {u,ν} \right)} \leqslant 0} \right. for b å _{u e V} b _u = 1 } \left. {\sum\nolimits_{uεV} {b_u = 1} } \right\} . Then, the rank of P is defined as the dimension of the smallest face of the cone H _{| V |} {\mathcal{H}}_{\left| V \right|} that contains d _P.

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