Worm Hole Model
This is a model of wormhole exiting from a two dimensional plane.
To soften the transition from plane to cylinder there's an intermediate cone with an angular deficit of pi.
Straight lines enter the hole. Some are "bent" by the cone and sent back out into the plane.
Others enter the cylinder. These cylindrical  geodesics are a variety of helixes.
The geodesics go to one part of the manifold from another in the fashion advised by
Geoffrey Landis on this page: 
This animation shows how to line up the flattened cone with the plane
when continuing light rays from plane to cone.
In Landis' illustration a circle with a wedge cut from it was used to make a cone.
My cones are a little different - I cut out a full circle, make one radial cut and then curl.
This way more of the geodesics can be drawn
and its easier to glue paper surface to surface than it is edge to edge.