= Solution
\b[There are two, two and four <stereoisomers>, respectively; all eight individual <stereoisomers> are <chiral>.] The drawings below give the mirror pairs. Solid and hashed wedges distinguish opposite faces; ordinary changes between conformers are not counted again.
* The benzyl-substituted alkylidenecyclohexane has an axial stereogenic element. At one end the exocyclic <alkene> presents Ph and H; at the other end the substituted ring <carbon> presents benzyl and H. The ring constrains the intervening paths, so exchanging one end pair gives the nonsuperposable mirror image. There is one enantiomeric pair, rather than an independent ordinary $E/Z$ pair multiplied by a carbon-center count.
* The diphenylspiro compound also has one <axial chirality>. The two four-membered rings occupy different, approximately perpendicular planes. Their remote Ph/H substitutions distinguish the two handed arrangements. It gives one enantiomeric pair and no meso form. <axial chirality> of this spiro framework is experimentally established, for example by resolution of its 2,6-dicarboxylic-acid derivatives.<Enantiopure spiro[3.3]heptane-2,6-dicarboxylic acid by Hong-Zhi Tang and others>[Abstract, isolation of enantiopure spiro derivatives]{ref}
* The phospholane has a stereogenic <carbon> at the COOH-bearing position and a pyramidal <phosphorus stereocenter>. The <phosphorus> has three different <carbon> ligands and a <lone pair>: its two ring paths differ because only one encounters the substituted <carbon> immediately. The four configurations are $(R_P,R_C)$, $(R_P,S_C)$, $(S_P,R_C)$ and $(S_P,S_C)$. The first and last form a mirror pair, as do the middle two. <carbon> and <phosphorus> cannot be interchanged by a <symmetry operation>, so there is no meso reduction in the count.
Unlike the usual rapidly inverting trialkylamine, a pyramidal <phosphine> can retain a <phosphorus> configuration on an ordinary observational timescale; its two <phosphorus> configurations must therefore be included.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2021/paper-1-b3-stereoisomers.png]
{title=Eight stereoisomers grouped into four mirror pairs, with axial and phosphorus stereochemistry shown}
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