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We consider a family
, of real hypersurfaces in a complex affine three-dimensional quadric arising in connection with the classification of homogeneous compact simply connected real-analytic hypersurfaces in
due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the Cauchy–Riemann (CR)-embeddability of
. In our earlier article, we showed that
is CR-embeddable in
. In the present paper, we prove that
can be immersed in
by means of a polynomial map. In addition, one of the immersions that we construct helps simplify the proof of the above CR-embeddability theorem and extend it to the larger parameter range
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