Are there any new platonic solids in non-euclidean space

[Bohandas]

I know thay in the 2 dimensional elliptic plane there are two additional regular polygons, the digon/lune, and the monogon/henagon.

Does this sort of effect extend into 3 dimensional elliptic space? Is there a regular elliptic polyhedron with fewer faces than the tetrahedron?

EDIT:
On further thought, it seems obvious that there must be a single-faced regular polyhedron in elliptic space that's just a flat plane extended until it contacts itself. But are there 2 faced or three faced regular polyhedra?

[gomipile]

I found this relatively quickly:

https://en.m.wikipedia.org/wiki/Dihedron

I find this topic interesting, so I might look further later.


Edit 1?:
https://en.m.wikipedia.org/wiki/Hosohedron#Hosotopes