Anyway, some shots of a very basic non-euclidean map I threw together in ol' UT some time ago just to see if it would handle it gracefully :prosperous: :
Overwiew - the map is is essentially a dodecahedron with opposite pairs of faces identified with each other with pi/5 twist (using warp zones to stitch the geometry with itself).
A burst of DP shots traveling around level.
Self.
A single Redeemer missile traveling around level.
Conclusion:
Old Unreal engine is - as you can see - surprisingly robust and good at withstanding abuse, but player pawn code would have to be modified to make crossing the boundaries truly seamless - as it is it doesn't map entry rotation to exit rotation properly, presumably by not allowing player pawn to roll, even transiently.