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Any set of 8 blocks of size 4 over an 8-set, isomorphic to $\{
abcd,abxy$, $acty, adtx$, $bcyz, bdxz, cdtz, txyz \}$ is called an
octahedral configuration which is a generalization of a
quadrilateral of Pasch configuration or one half of a minimal
$3$-$(8,4)$ trade. In this paper we show that all Hanai's
recursive constructions of SQS $(v)$ for $v\equiv 2$ or 4 (mod 6)
contain octahedrads except for $v=4,10$, and $14$.
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