Please stick with me on this convoluted post. I was helping a student solve this problem today and was temporarily stumped but I believe I figured it out. I'm trying to reconcile the formula for the maximum # of stereoisomers a compound can have with 1,2,3 trimethyl cyclopropane.
The formula for the maximum number of stereoisomers a compound can have is commonly said to be "2n - the number of meso compounds" where n is the number of stereocenters.
The definition of stereocener is "an atom where interchanging two groups give rise to stereoisomerism"
In 1,2,3 cyclopropane interchanging 2 groups on any of the carbons gives rise to stereoisomerism: there are two possible isomers, (cis,cis,trans) and (cis, cis, cis)), both of which are achiral.
But if the molecule has 3 stereocenters, acccording to the formula it should have 8 possible stereoisomers? This can't possibly be correct, even subtracting potential meso compounds. But there aren't any meso compounds, because none of the carbons are even chiral centers to begin with.
My interpretation here is that "n" in the formula really should be chiralcenters, not stereocenters. I believe some sources, including wikipedia, erroneously use chiral center and stereocenter synonymously when in fact they have different meanings. A chiral center can potentially give rise to chirality, where as a stereocenter gives rise to stereoisomerism. So every chiral center is a stereocenter, but not vice versa. Is this correct? Or is there a hole in my logic somewhere?