How to naturally connect objects of different shapes I want to connect objects of different shapes naturally. The part I'm going to connect to is the edge that has an empty face.

Edge bridge does not apply because it has different shapes.
Here is a way using Grid Fill.

UPDATE: check out the "Bridge Edge Loop" option proposed by @RayMairlot in the comments. It may be best suited to your need.

ref: https://docs.blender.org/manual/en/latest/modeling/meshes/editing/faces.html#grid-fill


Subdivide the side to match the number of vertices on the other side
Create supporting Edges
Select edges on both sides
Grid fill
repeat for the other sides.