Decalins are the most important members of group of molecules called fused rings. The name, as it might suggest, applies to molecules which have two adjacent rings, which have two atoms in common. Decalins are two fused cyclohexane rings, and can occur in two isomers: cis and trans:
The forms get their names from the relative position of the two hydrogen atoms indicated in either case (i.e. they are trans, or on opposite sides, in the first case, and cis, or on the same side, in the second case.)
The cis isomer is fused by an axial and an equatorial bond, however, the trans isomer is fused by two equatorial bonds. According to the earlier discussion of cyclohexane, we would expect that the trans isomer, with its two equatorial bonds would be the more stable of the two isomers, and this is indeed the case.
The trans isomer is conformationally rigid, that is, it cannot undergo ring-flipping, but the cis form (depending on its substituents) can undergo rapid ring-flipping. The trans form has a centre of symmetry, and is therefore optically inactive, whereas the cis form has no centre of symmetry in either of its two forms, and has non-superimposable mirror-images, so is optically active.
Determining relative stabilities of substituted decalins is more difficult than with cyclohexane i.e.:
With the 9-methyldecalin systems shown above, the trans has 1,3 diaxial interactions with 4 hydrogen atoms, and the cis with only 2, however, we have already established that the trans system is inherently more stable than the cis, so there is a balance of factors. The presence of other groups may shift the balance in either direction.