I read the answers to this very interesting question and saw that we can in fact embed the Euclidean plane into hyperbolic 3-space using what is called a horosphere. However, as Hilbert showed us, the reverse is not true; we cannot embed the hyperbolic plane into Euclidean 3-space. This made me interested in considering the other non-Euclidean geometry: elliptic geometry. We can embed the plane from elliptic geometry into Euclidean 3-space - the result is spherical geometry - but:
a) is the reverse true: can we embed the Euclidean plane into elliptic 3-space?
b) Furthermore, is it possible to embed the elliptic plane into hyperbolic 3-space?
c) What about the reverse: can we embed the hyperbolic plane into elliptic 3-space?