Is a $3D$ volume possible with only $3$ faces? I was wondering if a $3D$ volume with only $3$ faces was possible. I know that in the Euclidean space, it is technically not possible (the minimum being $4$ faces), but maybe there was some other way.
Like the moebius strip that only has one side and one face.
Maybe by bending the space?
Thank you!

I prepared this image for the version of your question asking for a volume with three vertices, which emphasizes mathreadler's comment "sure if you allow bending of surface":

A version with three faces is obtained by intersecting three spheres:

If you do not want to have bent faces, but you allow infinite faces: imagine a trianglular pyramid that extends infinitely in one direction. It has three faces only.
If you want to avoid bent and infinite faces, you might find a solution in sphereical geometries similar to the one in my second picture. I think that in spherical geometries, the bent faces of this shape are actually intrisically "flat" because bounded by great circles. Not completely sure though.
