= Solution
The cis fusion admits two chair–chair conformers, related by simultaneous <ring inversion>. The bridgehead <hydrogens> remain cis, while their axial/equatorial descriptions exchange. In one fold the <oxygen> next to the fusion occupies the concave, inside position; in the other, the corresponding inside position is occupied by a methylene group. Both chair-only structures are shown in the lower panels of the dioxane diagram.
\b[The O-inside chair–chair conformer is strongly favored.] In the unfavorable fold, the inward methylene and its C–H bonds create close nonbonded contacts with the other ring, analogous to costly 1,3-diaxial/gauche contacts in cis-<decalin>. Placing <oxygen> in that location removes the corresponding <carbon>-bound <hydrogens> and reduces the obstruction. The comparison is between the two conformers of the same cis <configuration>; making the fusion trans would be a configurational change, not a chair flip. Nor is it appropriate to flatten both six-membered rings into regular hexagons, which would hide the decisive inside contacts.
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