= Orthogonality of hypercube body diagonals
{title2=$u\cdot v=n-2h$}
Two sign-vector vertices of a centered <hypercube> differing in $h$ coordinates have <dot product> $n-2h$. Thus their body diagonals can be <orthogonal> only in even dimension. A collection of mutually <orthogonal> nonzero diagonals has at most $n$ members; achieving $n$ is equivalent to the existence of a <Hadamard matrix> of order $n$. For unoriented lines the angle is determined by $|n-2h|/n$, while oriented vertex vectors retain the sign of their <dot product>.
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