= Borsuk counterexample in dimension 1325
{c}
{title2=$d=\binom{52}{2}-1=1325$}
Use the <balanced cut-vector distance formula> with $p=13$. There are $\binom{51}{25}=247959266474052$ distinct cuts. A subset of strictly smaller <diameter> contains no pair with side intersection thirteen, so deleting their shared coordinate one and applying the <Frankl-Wilson theorem> bounds its size by $\binom{51}{12}=158753389900$. At least 1562 smaller-diameter parts are needed, exceeding $1325+1$. The cut vectors occupy an <affine hyperplane> in $\mathbb R^{1326}$, which identifies isometrically with $\mathbb R^{1325}$ and gives the stated explicit counterexample.
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