How many stereoisomers can exist for cortisone?

Cortisone can be found on wikipedia. I’ve redrawn the structure below, with standard steroid numbering. Noting that ##sp^3## carbons are potential chiral centers, I’ve marked them.

Carbon-8: S
Carbon-9: S
Carbon-10: R
Carbon-13: S
Carbon-14: S
Carbon-17: R

So, we see six stereocenters. We also don’t see any carbons that can allow any cis-trans geometric isomers. Finally, there is no plane of symmetry anywhere here. So, with that in mind, the number of stereounits (stereocenters + cis-trans centers) is still six.

The number of stereoisomers is known to be ##2^n – “meso structures”##, but since there is no plane of symmetry, it is just ##2^n##, where ##n## is the number of stereounits.

Thus, ##2^6 = color(blue)(64)## stereoisomers.

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